1 - 10 students are to be seated in two rows equally for the Mock test in a room. There are two sets of papers, Code A and Code B. each of two rows can have only one set of paper but different that from o
7257600
2 - 12 chairs are arranged in a row and are numbered 1 to 12. 4 men have to be seated in these chairs so that the chairs numbered 1 to 8 should be occupied and no two men occupy adjacent chairs. Find the
384
3 - 12 people at a party shake hands once with everyone else in the room.How many handshakes took place?
66
4 - 139 person have signed for an elimination tournament. All players are to be paired up for the first round but because 139 is an odd number one player gets a bye, which promotes him to the second round
138
5 - 2 men and 1 woman board a bus of which 5 seats are vacant, one of these 5 seats is reserved for ladies. A woman may or may not sit on the seat reserved for ladies, In how many different ways can the five seats be occupied by these passengers?
36
6 - 2 Men and 1 women board a bus in which 5 seats are vacant, one of these 5 seats is reserved for ladies. A women may or may not sit on the seat reserved for ladies . In how many different ways can the
36
7 - 20 persons were invited to a party. In how many ways, they and the host can be seated at a circular table ?
20 !
8 - 5 children are to be seated on a bench. In how many ways can it be done if the eldest child always sits in the middle?
24
9 - 5 children are to be seated on one bench. In how many ways can it be done?
120
10 - A bag contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the bag, if at least one black ball is to be included in the draw?
64
11 - A box contains 10 balls out of which 3 are red and rest are blue. In how many ways can a random sample of 6 balls be drawn from the bag so that at the most 2 red balls are included in the sample and n
168
12 - A box contains 2 white balls and 4 red ball. in how many ways can 3 balls be drawn from the box , if at least one black ball is to be included i the draw ?
64
13 - A box contains 4 red, 3 white and 2 blue balls. Three balls are drawn at random. Find out the number of ways of selecting the balls of different colours?
24
14 - A boy has nine trousers and 12 shirts. In how many different ways can he select a trouser and a shirt?
108
15 - A boy has nine trousers and 12 shirts. In how many different ways can he select a trouser and a shirt?
108
16 - A child has four pockets and three marbles. In how many ways, the child can put the marbles in the pockets ?
64
17 - A coach must choose five starters from a team of 12 players. How many different ways can the coach choose the starters ?
729
18 - A coin is tossed 3 times. Find out the number of possible outcomes.
8
19 - A college has 10 basketball players. A 5-member team and a captain will be selected out of these 10 players. How many different selections can be made?
1260
20 - A committee has 5 men and 6 women. What are the number of ways of selecting 2 men and 3 women from the given committee?
200
21 - A committee has 5 men and 6 women. What are the number of ways of selecting 2 men and 3 women from the given committee?
200
22 - A committee is to be formed comprising 7 members such that there is a simple majority of men and at least 1 woman. The shortlist consists of 9 men and 6 women. In how many ways can this committee be f
4914
23 - A committee of 5 persons is to be formed from 6 men and 4 women. In how many ways can this be done when at least 2 women are included ?
186
24 - A Committee of 5 persons is to be formed from a group of 6 gentlemen and 4 ladies. In how many ways can this be done if the committee is to be included atleast one lady?
246
25 - A delegation of 5 members has to be formed from 3 ladies and 5 gentlemen. In how many ways the delegation can be formed, if 2 particular ladies are always included in the delegation?
20
26 - A delegation of 5 members has to be formed from 3 ladies and 5 gentlemen. In how many ways the delegation can be formed, if 2 particular ladies are always included in the delegation?
20
27 - A department had 8 male and female employees each. A project team involving 3 male and 3 female members needs to be chosen from the department employees. How many different projects teams can be chose
3136
28 - A family consist of a grandfather, 5 sons and daughter and 8 grandchildren. They are to be seated in a row for dinner. The grandchildren wish to occupy the 4 seats at each end and the grandfather refu
8! * 480
29 - A group consists of 4 men, 6 women and 5 children. In how many ways can 2 men , 3 women and 1 child selected from the given group?
600
30 - A group consists of 4 men, 6 women and 5 children. In how many ways can 2 men , 3 women and 1 child selected from the given group?
600
31 - A group consists of 4 men, 6 women and 5 children. In how many ways can 3 men, 2 women and 3 children selected from the given group?
600
32 - A group consists of 4 men, 6 women and 5 children. In how many ways can 3 men, 2 women and 3 children selected from the given group?
600
33 - A group of 10 representatives is to be selected out of 12 seniors and 10 juniors. In how many different ways can the group be selected if it should have at least one senior?
²²C₁₀ – 1
34 - A group of 10 representatives is to be selected out of 12 seniors and 10 juniors. In how many different ways can the group be selected, if it should have 5 seniors and 5 juniors?
¹²C₇ * ¹⁰C₅
35 - A letter lock consists of three rings each marked with six different letters. The number of distinct unsuccessful attempts to open the lock is at the most -.
215
36 - A library has two books each having three copies and three other books each having two copies. In how many ways can all these books be arranged in a shelf so that copies of the same book are not separ
120
37 - A local delivery company has three packages to deliver to three different homes. if the packages are delivered at random to the three houses, how many ways are there for at least one house to get the
5
38 - A man has 9 friends, 4 boys and 5 girls. In how many ways can he invite them, if there have to be exactly 3 girls in the invitees ?
160
39 - A man positioned at the origin of the coordinate system. the man can take steps of unit measure in the direction North, East, West or South. Find the number of ways of he can reach the point (5,6), co
462
40 - A man wants to go abroad by ship and return by air. He has a choice of 4 ships to go and 5 airlines to return. In how many ways can man perform his journey?
20
41 - A mixed doubles tennis game is to be played two teams(each consists of one male and one female) There are four married couples. No team is to consist a husband and his wife. What is the maximum number of games that can be played?
42
42 - A person ordered 5 pairs of black socks and some pairs of brown socks. The price of a black pair was thrice that of a brown pair while preparing the bill the bill clerk inter-changed the number of black and brown pairs by mistake which increased the bill
25
43 - A question paper consists of five problems, each problem having three internal choices. In how many ways can a candidate attempt one or more problems?
1023
44 - A question paper consists of three sections 4,5 and 6 questions respectively. Attempting one question from each section is compulsory but a candidate need not attempt all the questions. In how many wa
29295
45 - A question paper had 10 questions. Each question could only be answered as True (T) or false (F). Each candidate answered all the questions. Yet, no two candidate wrote the answers in an identical seq
1024
46 - A question paper had 10 questions. Each question could only be answered as true(T) of False(F). Each candidate answered all the questions, Yet no two candidates wrote the answers in an identical sequence. How many different sequences of answers are possib
1024
47 - A question paper has two parts P and Q, each containing 10 questions. If a student needs to choose 8 from part P and 4 from part Q, in how many ways can he do that?
9450
48 - A question paper has two parts, A and B, each containing 10 questions. If a student has to choose 8 from part A and 5 from part B, in how many ways can he choose the questions?
11340
49 - A selection committee is to be chosen consisting of 5 ex-technicians. Now there are 12 representatives from four zones. It has further been decided that if Mr. X is selected, Y and Z will not be selec
672
50 - A selection is to be made for one post of principal and two posts of vice-principal amongst the six candidates called for the interview only two are eligible for the post of principal while they all are eligible for the post of vice-principal. The number
None of these
51 - A student has to opt for 2 subjects out of 5 subjects for a course. Namely commerce, economics, statistics, mathematics 1 and Mathematics 2, Mathematics 2 can be offered only if mathematics 1 has also opted. The number of different combinations of two sub
7
52 - A tea expert claims that he can easily find out whether milk or tea leaves were added first to water just by tasting the cup of tea. In order to check this claims 10 cups of tea are prepared, 5 in one
252
53 - A tea expert claims that he can easily find out whether milk or tea leaves were added first to water just by tasting the cup of tea. In order to check this claims 10 cups of tea are prepared, 5 in one
252
54 - A teacher of 6 students takes 2 of his students at a time to a zoo as often as he can, without taking the same pair of children together more than once. How many times does the teacher go to the zoo?
15
55 - A team of 16 cricketers is collected for the ODI series. It consists of 10 old players and 6 new players. As a principle it was decided that the team playing any of the matches must contain 8 players,
900
56 - A team of 8 students goes on an excursion, in two cars, of which one can seat 5 and the other only 4. In how many ways can they travel?
126
57 - A two member committee comprising of one male and one female member is to be constitute out of five males and three females. Amongst the females. Ms. A refuses to be a member of the committee in which
14
58 - A two number committee comprising of one male and the female number is to be constituted out of five male and 3 females. Amongst the females, Ms. A refused to be number committee in which Mr.B is taken as the number of how many different ways can the comm
14
59 - A, B , C , and D are four towns, any three of which are non-collinear. Then, the number of ways to construct three roads each joining a pair of towns, so that the roads do not form a triangle, is ?
24
60 - A, B, C and D are four non-coplanar points. The number of planes that can be drawn passing through any three of these points, is
4
61 - After every get-together every person present shakes the hand of every other person. If there were 105 handshakes in all, how many persons were present in the party?
15
62 - An event manager has ten patterns of chairs and eight patterns of tables. In how many ways can he make a pair of table and chair?
80
63 - Boxes numbered 1, 2, 3, 4 and 5 are kept in a row and they are to be filled with either a red or a blue ball such that no two adjacent boxes can be filled with blue balls Then, how different arrangeme
22
64 - Consider the word ROTOR. Whichever way you read it, from left to right or from right to left, you get the same word. Such a word is known as palindrome. Find the maximum possible number of 5-letter pa
17576
65 - Evaluate 25!/23!
600
66 - Everybody in a room shakes hands with everybody else. The total number of hand shakes is 66. The total number of persons in the room is ?
12
67 - Find out the number of ways in which 6 rings of different types can be worn in 3 fingers?
729
68 - Find the no. ofways in which 4 identical balls can be distributed among 6 identical boxes, if not more than one ball goes into a box?
15
69 - Find the no.of ways in which a committee consisting of 3 Men and 2 Women can be formed from 5 Men and 4 Women?
5c3 x 4c2
70 - Find the number of diagonals formed in hexagon .
9
71 - Find the number of different ways of forming a committee consisting of 3 men and 3 women from 6 men and 5 women. ?
30
72 - Find the number of triangles which can be formed by joining the angular points of a polygon of 8 sides as vertices.
56
73 - Find the number of ways in which 5 players out of 8 players can be selected to form a team.
56
74 - Find the number of ways in which 8064 can be resolved as the product of two factors?
24
75 - Find the number of ways of arranging the host and 8 guests at a circular table, so that the host always sits in a particular seat ?
8!
76 - Find the number of ways of arranging the letters of the word "MATERIAL" such that all the vowels in the word are to come together?
1440
77 - Find the number of ways of arranging the letters of the word “MATERIAL” such that all the vowels in the word are to come together?
1440
78 - Find the number of ways of preparing a chain with 5 different coloured beads ?
12
79 - Find the number of ways, in which 12 different beads can be arranged to form a necklace .
11 !/2
80 - Find the total number of distinct vehicle numbers that can be formed using two letters followed by two numbers. Letters need to be distinct.
65000
81 - Find the value of 12p2, 9p1, 8p8?
132,9,8!
82 - Find the value of 3p1?
3
83 - Find the value of 9p4?
3024
84 - For a group photograph, 3 boys and 4 girls stand in a line in all possible ways. How many photos could be taken if each photo corresponds to each such arrangement?
5040
85 - From 6 men and 4 ladies, a committee of 5 is to be formed. In how many ways can this be done, if the committee is to include at least one lady?
246
86 - From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?
756
87 - From a group of 7 men and 6 women, tive persons are to be selected to form a committee to that atleast 3 men are there on the committee. In how many ways can it be done?
756
88 - From a total of six men and four ladies a committee of three is to be formed. If Mrs. X is not willing to join the committee in which Mr. Y is a member, whereas Mr.Y is willing to join the committee o
91
89 - Groups each containing 3 boys are to be formed out of 5 boys. A, B, C, D and E such that no group can contain both C and D together. What is the maximum number of such different groups?
7
90 - Groups, each containing 3 boys are to be formed out of 5 boys, A, B , C, D and E such that no group can contain both C and D together. What is the maximum number of such different groups ?
7
91 - How many 3 – digit number can be formed from the digit 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated?
20
92 - How many 3 digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9 which are divisible by 5 and none of the digits is repeated?
20
93 - How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9 which one divisible by 5 and none of the digits is repeated?
20
94 - How many 3-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed?
720
95 - How many 4letter code can be formed using the first 9 letters of the English alphabets, if no letter can be repeated?
3024
96 - How many 4-letter words with or without meaning, can be formed out of the letters of the word, ‘LOGARITHMS’, if repetition of letters is not allowed?
5040
97 - How many 4-letter words with or without meaning, can be formed out of the letters of the word, ‘LOGARITHMS’, if repetition of letters is not allowed?
5040
98 - How many 4-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed?
5040
99 - How many 5-digit positive integers exist the sum of whose digits are odd?
45000
100 - How many 6 digit number can be formed from the digits 1, 2, 3, 4, 5, 6 which are divisible by 4 and digits are not repeated?
192
101 - How many 6 digit telephone numbers can be formed if each number starts with 35 and no digit appears more than once?
1680
102 - How many 6 letter words can be formed with the letters of the word 'POLICY' such that the vowels occur only at even places.
144
103 - How many alphabets need to be there in a language if one were to make 1 million distinct 3 digit initials using the alphabets of the language?
100
104 - How many arrangements can be made out of the letters of the word COMMITTEE, taken all at a time, such that the four vowels do not come together?
43200
105 - How many arrangements can be made out of the letters of the word DRAUGHT, the vowels never beings separated?
1440
106 - How many arrangements can be made out of the letters of the word 'ENGINEERING' ?
277200
107 - How many arrangements of four 0's (zeroes), two 1's and two 2's are there in which the first 1 occur before the first 2?
210
108 - How many arrangements of the letters of the word ‘BENGALI’ can be made if the vowels are never together.
720
109 - How many arrangements of the letters of the word ‘BENGALI’ can be made if the vowels are to occupy only odd places.
576
110 - How many arrangements of the letters of the word BEGIN can be made, without changing the place of the vowels in the word?
6 ways
111 - How many diagonals can be drawn in a heptagon?
14
112 - How many diagonals can be drawn in a pentagon?
5
113 - How many different five-letter words can be formed using the letter from the world APPLE?
60
114 - How many different four letter words can be formed (the words need not be meaningful using the letters of the word "MEDITERRANEAN" such that the first letter is E and the last letter is R?
59
115 - How many different letter arrangements can be made from the letter of the word RECOVER ?
1260
116 - How many different numbers can be formed from the digits 3, 4, 5, 6 and 7 when repetitions are allowed ?
3905
117 - How many different words beginning with O and ending with E can be formed with the letters of the word ORDINATE, so that the words are beginning with O and ending with E?<
8!
118 - How many different words can be formed with the letters of the word EQUATION without changing the relative order of the vowels and consonants?
720
119 - How many different words can be formed with the letters of the word 'TOMORROW', taking all at a time ,
3000
120 - How many different words can be made using the letters of the word ' HALLUCINATION ' if all constants are together?
1587600
121 - How many even numbers of three digits can be formed with the digits 0, I, 2, 3, 4, 5 and 6?
30
122 - How many four digit even numbers can be formed using the digits {2, 3, 5, 1, 7, 9}
60
123 - How many integers, greater than 999 but not greater than 4000, can be formed with the digits 0, 1, 2, 3 and 4, if repetition of digits is allowed?
376
124 - How many lines can you draw using 3 non collinear (not in a single line) points A, B and C on a plane?
3
125 - How many necklace of 12 beads each can be made from 18 beads of different colours?
18!(6 x 24)
126 - How many necklaces of 12 beads can be made from 18 beads of various colours ?
[119 x 13!] / 2
127 - How many nos. greater than 800 and less than 4000 can be made with the digits 0, I, 2, 4, 5, 7, 8, 9, no number (digit) occurring more than once in the same number?
504
128 - How many number plates of 3 digits can be formed with four digits 1, 2, 3 and 4?
24
129 - How many numbers of five digits can be formed with the digits 0, 1, 2, 3, 4, 6 and 8?
2160
130 - How many numbers of five digits can be formed with the digits 0, 2, 4, 6 and 8?
96
131 - How many numbers of five digits can be formed with the digits 1, 3, 5, 7 and 9, no digit being repeated?
120
132 - How many Permutations of the letters of the word APPLE are there?
60
133 - How many quadrilaterals can be formed by joining the vertices of an octagon?
70
134 - How many three letter computer passwords can be formed (no repetition allowed) with at least one symmetric letter ?
12870
135 - How many three letter words are formed using the letters of the word TIME
24
136 - How many three letter words are formed using the letters of the word TIME?
24
137 - How many triangles can be formed with 8 non-collinear points lying in a plane?
56
138 - How many triangles can be formed with four points (A, B, C & D) in a plane? It is given that no three points are collinear. From the three points A, B and C, have only one triangle with these
4
139 - How many ways can 10 letters be posted in 5 post boxes, if each of the post boxes can take more than 10 letters ?
5C5
140 - How many ways can 4 prizes be given away to 3 boys, if each boy is eligible for all the prizes?
24
141 - How many words beginning with vowels can be formed with the word EQUATION?
25200
142 - How many words can be formed by re-arranging the letters of the word ASCENT such that A and T occupy the first and last position respectively?
4!
143 - How many words can be formed by using all letters of the word ‘BIHAR’ ?
120
144 - How many words can be formed by using all letters of the word 'BIHAR'?
120
145 - How many words can be formed with the letters of the word EQUATION?
40320
146 - How many words can be formed with the letters of the word INTERNATIONAL?
129729600
147 - How many words with or without meaning, can be formed by using all the letters of the word, 'DELHI' using each letter exactly once?
120
148 - How many words, can be formed from the letters of the word 'EXTRA' so that the vowels one never together?
1365
149 - I have an amount of Rs 10 lakh, which I went to invest in stocks of some companies. I always invest only amounts that are multiples of Rs 1 lakh in the stock of any company. If I can choose from among
1001
150 - If (m+n)p4 = 3024, (m-n)p4 = 120, find m and n.
7,2
151 - If 7pr = 210, find r?
3
152 - If all the numbers 2, 3, 4, 5, 6, 7, 8 are arranged, find the number of arrangements in which 2, 3, 4, are together?
720
153 - If letters of the work KUBER are written in all possible orders and arranged as in a dictionary, then the rank of the word KUBER will be:
67
154 - If nc2 = nc5, find n?
7
155 - If np3 = 210, find n.
7
156 - If the letters of the word CHASM are rearranged to form 5 letter words such that none of the word repeat and the results arranged in ascending order as in a dictionary what is the rank of the word CH
32
157 - If the letters of the word CHASM are rearranged to form 5 letter words such that none of the word repeat and the results arranged in ascending order as in a dictionary what is the rank of the word CHA
32
158 - If the letters of the word PLACE are arranged taken all at a time, find how many do not start with AE.
114
159 - If the letters of the word SACHIN are arranged in all possible ways and these words are written out as in dictionary, then the word ‘SACHIN’ appears at serial number :
601
160 - If there are 10 positive real numbers n1 < n2, n3 .... < n10 How many triplets of these numbers (n1, n2, n3) (n2, n3, n4), ... can be generated such that in each triplet the first number is always les
120
161 - If there are 12 persons in a party and each of them shakes hands with each other, how many handshakes do happen in the party?
66
162 - If there are 15 dots on a circle,how many triangles can be formed?
455
163 - In a box, there are 5 black pens, 3 white pens and 4 red pens. In how many ways can 2 black pens, 2 white pens and 2 red pens can be chosen?
180
164 - In a class there are 20 boys and 25 girls. In how many ways can a boy and a girl be selected?
500
165 - In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?
209
166 - In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?
209
167 - In a hockey championship, there are 153 matches played. Every two team played one match with each other. The number of teams participating in the championship is:
18
168 - In a monthly test, the teacher decides that there will be there questions, one each from ex. 7, 8 and 9 of the text book. There are 12 questions in ex-7 , 18 in ex-8 and 9 in ex-9. In how many ways ca
1944
169 - In a party every person shakes hand with every other person. If there was a total of 210 handshakes in the party, find the no. of persons who were present in the party.
21
170 - In a party every person shakes hands with every other person. If there are 105 hands shakes, find the number of person in the party.
15
171 - In a Plane there are 37 straight lines, of which 13 pass through the point A and 11 pass through the point B. Besides, no three lines pass through one point, no lines passes through both points A and
535
172 - In a question paper, there are four multiple choice type question. Each question has five choices with only one choice for its correct answer. What is the total number of ways in which a candidate wil
624
173 - In a question paper, there are four multiple choice type questions, each question has five choices with only one choice for it’s correct answer. What is the total number of ways in which a candidate will not get all the four answers correct?
624
174 - In a railway compartment, there are 2 rows of seats facing each other with accommodation for 5 in each, 4 wish to sit facing forward and 3 facing towards the rear while 3 others are indifferent. In ho
43200
175 - In an examination paper, there are two groups each containing 4 questions. A candidate is required to attempt 5 questions but not more than 3 questions from any group. In how many ways can 5 questions
48
176 - In how many difference ways can six players be arranged in a line such that two of them, Abhinav and Manjesh are never together ?
360
177 - In how many different number of ways 4 boys and 2 girls can sit on a bench?
720
178 - In how many different number of ways 4 boys and 3 girls can sit on a bench such that girls always sit together.
720
179 - In how many different number of ways 5 men and 2 women can sit on a shopa which can accommodate persons?
210
180 - In how many different number of ways a combination of 3 men and 2 women can be selected from 6 men and 5 women.
25
181 - In how many different number of ways a Committee of 3 person of can be selected from 5 men and 3 women such that atleast 1 women is included in the committee.
46
182 - In how many different number of ways the letters of the word 'ENGINEERING' can be arranged.
277200
183 - In how many different number of ways the letters of the word 'ENGINEERING' can be arranged. In how many different number of ways a combination of 3 persons can be selected from 4 men and 2 women.
200
184 - In how many different ways , can the letters of the word 'VENTURE' be arranged?
2520
185 - In how many different ways can 2 boys and 4 girls be arranged in a row such that all the boys stand together and all the girls stand together?
96
186 - In how many different ways can 2 vowels and 3 consonants can be selected from 4 vowels and 10 consonants?
4c2 x 10 c 3
187 - In how many different ways can 5 girls and 5 boys form a circle such that the boys and the girls alternate?
2880
188 - In how many different ways can four books A, B, C and D be arranged one above another in a vertical order such that the books A and B are never in continuous position ?
12
189 - In how many different ways can four books A, B, C and D be arranged one above another in a vertical order such that the books A and B are never in continuous position?
12
190 - In how many different ways can six players be arranged in a line such that two of them, Asim and Raheem are never together?
480
191 - In how many different ways can the letters 'DETAIL' be arranged in such a way that the vowels occupy only the odd positions
36
192 - In how many different ways can the letters of the word ' cloud' can be arranged?
120
193 - In how many different ways can the letters of the word "CLAIM" be rearrangement?
120
194 - In how many different ways can the letters of the word ‘MATHEMATICS’ be arranged so that the vowels always come together?
120960
195 - In how many different ways can the letters of the word ‘OPTICAL’ be arranged so that the vowels always come together?
720
196 - In how many different ways can the letters of the word 'ABILITY' can be arranged?
2520
197 - In how many different ways can the letters of the word 'BELIEVE' be arranged?
840
198 - In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together?
50400
199 - In how many different ways can the letters of the word 'DETAIL' be arranged such that the vowels must occupy only the odd positions?
36
200 - In how many different ways can the letters of the word ENTRANCE be arranged?
10080
201 - In how many different ways can the letters of the word 'JUDGE' be arranged such that the vowels always come together?
48
202 - In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together?
720
203 - In how many different ways can the letters of the word 'LEADING' be arranged such that the vowels should always come together?
720
204 - In how many different ways can the letters of the word 'MACHINE' be arranged?
5040
205 - In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together?
120960
206 - In how many different ways can the letters of the word 'MATHEMATICS' be arranged such that the vowels must always come together?
120960
207 - In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?
720
208 - In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?
720
209 - In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?
720
210 - In how many different ways can the letters of the word 'PART' be arranged?
24
211 - In how many different ways can the letters of the word 'RUMOUR' be arranged?
180
212 - In how many different ways can the letters of the word 'SCHOOL' be arranged so that the vowels always come together?
120
213 - In how many different ways can the letters of the word 'TROUBLE' be arranged?
5040
214 - In how many different ways can the letters ofthe word 'OPTICAL' be arranged to that the vowels always come together?
4320
215 - In how many different ways, 5 boys and 5 girls can sit on a circular table, so that the boys and girls are alternate ?
2880
216 - In how many ways 2 students can be chosen from the class of 20 students?
190
217 - In how many ways 4 boys and 3 girls can be seated in a row so that they are alternate.
144
218 - In how many ways 6 different colored beads can be arranged in a necklace?
60
219 - In how many ways 8 persons can sit around a round dining table in such a manner that all will not have the same neighbors in any two arrangement?
2520
220 - In how many ways a committee of 5 members can be selected from 6 men and 5 ladies lowering of 3 men and 2 ladies?
200
221 - In how many ways a committee, consisting of 5 men and 6 women can be formed from 8 men and 10 women?
11760
222 - In how many ways a committee, consisting of 5 men and a women can be formed form 8 men and 4 women?
11760
223 - In how many ways a committee,consisting of 5 men and 6 women can be formed from 8 men and 10 women?
11760
224 - In how many ways ca live boys and three girls sit in a row such that all boys sit together?
2880
225 - In how many ways can 21 books on English and 19 books on Hindi be placed in a row on a shelf so that two books on hindi may not be together?
1540
226 - In how many ways can 3 people be seated in a row containing 6 seats?
120
227 - In how many ways can 4 boys and 5 girls be seated in a row so that they are alternate?
2880
228 - In how many ways can 5 different toys be packed in 3 identical boxes such that no box is empty, if any of the boxes may hold all of the toys ?
25
229 - In how many ways can 5 different toys be packed in 3 identical boxes such that no box is empty, if any of the boxes may hold all of the toys?
25
230 - In how many ways can 5 man draw water from 5 taps if no tap can be used more than once?
120
231 - In how many ways can 8 Indians and, 4 American and 4 Englishmen can be seated in a row so that all person of the same nationality sit together?
3! 4! 8! 4!
232 - In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?
63
233 - In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?
63
234 - In how many ways can a group of 5 men and 2 women be made out of a total of7 men and 3 women?
63
235 - In how many ways can an animal trainer arrange 5 lions and 4 tigers in a row so that no two lions are together?
2880
236 - In how many ways can live boys and three girls sit in a row such that all boys sit together?
2880
237 - In how many ways can Ram choose a vowel and a constant from the letters of the word ALLAHABAD?
4
238 - In how many ways can six different rings be worn on four fingers of one hand?
15
239 - In how many ways can the letter of the word ' civilization' be arranged ?
12! / 4! -1
240 - In how many ways can the letters of the word EDUCATION be rearranged so that the relative position of the vowels and consonants remain the same as in the word EDUCATION?
4! x 5!
241 - In how many ways can the letters of the word 'LEADER' be arranged?
360
242 - In how many ways can three consonants and two vowels be selected from the letters of the word "TRIANGLE"?
20
243 - In How many ways is it possible to make a selection by taking any number of 15 fruits, namely 3 oranges, 5 apples and 7 mangoes?
191
244 - In how many ways, a committee of 3 men and 2 women can be formed out of a total of 4 men and 4 women ?
24
245 - In how many ways, a cricket team of 11 players can be made from 15 players, if a particulars player is always chosen ?
1001
246 - In how many ways, can the letters of the word 'ASSASSINATION' be arranged, so that all the S are together ?
151200
247 - Letters of the word DIRECTOR are arranged in such a way that all the vowels come together. Find out the total no. of ways for making such arrangement. ?
2160
248 - Number of ways in which the letters of word GARDEN can be arranged with vowels in alphabetical order, is
360
249 - Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
25200
250 - Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
25200
251 - Out of eight crew members three particular members can sit only on the left side. Another two particular members can sit only on the right side. Find the number of ways in which the crew can be arrang
1728
252 - Six points are marked on a straight line and five points are marked on another line which is parallel to the first line. How many straight lines, including the first two, can be formed with these poin
30
253 - Six points are marked on a straight line and five points are marked on another line which is parallel to the first line. How many straight lines, including the first two, can be formed with these points?
32
254 - Suppose 7 students are staying in a hall in a hostel and they are allotted 7 beds. Among them, Parvin does not want a bed next to Anju because Anju snores. Then, in how many ways can you allot the bed
3600
255 - Suppose you want to arrange your English, Hindi, Mathematics, History, Geography and Science books on a shelf. In how many ways can you do it?
720
256 - Ten different letters of alphabet are given, words with 5 letters are formed from these given letters. Then, the number of words which have at least one letter repeated is:
69760
257 - The Indian Cricket team consists of 16 players. It includes 2 wicket keepers and 5 bowlers. In how many ways can a cricket eleven be selected if we have to select 1 wicket keeper and atleast 4 bowlers
1092
258 - The letter of the word LABOUR are permuted in all possible ways and the words thus formed are arranged as in a dictionary. What is the rank of the word LABOUR?
242
259 - The number of all possible words that can be formed using the letters of the word 'MATHEMATICS', is
11!/(2! x 2! x 2!)
260 - The number of arrangements that can be made with the letters of the word MEADOWS so that the vowels occupy the even places?
144
261 - The number of arrangements that can be made with the letters of the word MEADOWS so that the vowels occupy the even places?
144
262 - The number of circles that can be drawn out of 10 points of which 7 are collinear is
85
263 - The number of different permutations of the word 'BANANA' is ?
60
264 - The number of new words that can be formed by rearranging the letters of the word ‘ALIVE’ is__________?
119
265 - The number of new words that can be formed by rearranging the letters of the word 'ALIVE' is -.
119
266 - The number of permutations of the letters of the word ‘MESMERISE’ is___________?
9!/(2!)2 3!
267 - The number of positive integers which can be formed by using any number of digits from 0,1,2,3,4,5 without repetition.
1630
268 - The number of sequences in which 7 players can throw a ball, so that the youngest player may not be the last is -.
4320
269 - The number of sequences in which 7 players can throw a ball, so that the youngest player may not be the last is -.
4320
270 - The number of triangles that are formed by choosing the vertices from a set of 12 points, seven of which lie on the same straight line, is
185
271 - The number of ways in which a couple can sit around a table with 6 guests if the couple take consecutive seat is
1440
272 - The number of ways in which six boys and six girls can be seated in a row for a photograph so that no two girls sit together is -.
360
273 - The numbers of straight lines can be formed out of 10 points of which 7 are collinear ?
25
274 - The value of 75P2 is
5550
275 - There are 10 person among whom two are brother. The total number of ways in which these persons can be seated around a round table so that exactly one person sit between the brothers , is equal to:
2!*7!
276 - There are 10 points in a plane out of which 4 are collinear. Find the number of triangles formed by the points as vertices.
116
277 - There are 18 stations between Hyderabad and Bangalore. How many second class tickets have to be printed, so that a passenger can travel from any station to any other station?
380
278 - There are 20 books of which 4 are single volumes and the other are books of 8, 5 and 3 volumes respectively. In how many ways can all these books be arranged on a self so that volumes of the same book
7! 8! 5! 3!
279 - There are 30 people in a group. If all shake hands with one another , how many handshakes are possible?
435
280 - There are 4 boys and 4 girls. In how many ways can they be seated in a row so that all the girls do not sit together?
37440
281 - There are 5 candidates in an election and 3 of them are tobe elected. A voter can cast any number of votes but notmore than three. The number of ways in which he can cast his vote is
25
282 - There are 5 novels and 4 biographies. In how many ways can 4 novels and 2 biographies can be arranged on a shelf ?
21600
283 - There are 5 routes from place A to B and 2 routes from place B to C. Find how many routes are there from place A to C via B?
10
284 - There are 7 non-collinear points. How many triangles can be drawn by joining these points?
35
285 - There are 8 men and 10 women and you need to form a committee of 5 men and 6 women. In how many ways can the committee be formed?
11760
286 - There are five women and six men in a group. From this group a committee of 4 is to be chosen. How many different ways can a committee be formed that contain three women and one man?
60
287 - There are fourteen juniors and twenty-three seniors in the Service Club. The club is to send four representatives to the State Conference. If the members of the club decide to send two juniors and two
23023
288 - There are three prizes to be distributed among five students. If no students gets more than one prize, then this can be done in:
10 ways
289 - There are two identical red, two identical black, and two identical white balls.In how many different ways can the balls be placed in the cells (Each cell to contain one ball) shown above such that balls of the same colour do not occupy any two consecutiv
24
290 - There is a polygon of 12 sides . How many triangles can be drawn using the vertices of polygon ?
220
291 - Three dice (each having six faces with each face having one number from 1 or 6 ) are rolled. What is the number of possible outcomes such that atleast one dice shows the numbers 2 ?
91
292 - Three dice (each having six faces with each face having one number from 1 or 6) are ralled. What is the number of possible outcomes such that atleast one dice shows the number 2?
91
293 - Three flags each of different colours are available for a military exercise, Using these flags different codes can be generated by waving I. Single flag of different colours II. Any two flags in a different sequence of colours. III. three flags in a diffe
15
294 - Three gentlemen and three ladies are candidates for two vacancies. A voter has to vote for two candidates. In how many ways can one cast his vote?
15
295 - Twelve people from a club, by picking lots. One of them will host a dinner for all once in a month. The number of dinners a particular member has to host in one year is________?
Cannot be determined
296 - Using all the letters of the word "THURSDAY", how many different words can be formed?
8!
297 - Using all the letters of the word “NOKIA”, how many words can be formed, which begin with N and end with A?
6
298 - Using all the letters of the word “THURSDAY”, how many different words can be formed?
8!
299 - What are the number of ways to select 3 men and 2 women such that one man and one woman are always selected?
30
300 - What is the total number of ways in which Dishu can distribute 9 distinct gifts among his 8 distinct girlfriends such that each of them gets at least one gift?
36 * 8!
301 - When four fair dice are rolled simultaneously, in how many outcomes will at least one of the dice show 3?
671
302 - When six fair coins are tossed simultaneously, in how many of the outcomes will at most three of the coins turn up as heads?
42
303 - When six fairs coins are tossed simultaneously, in how many of the outcomes will at most three of the coins turn up as heads ?
42
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