Permutations and Combinations

A person has three different bags and four different books. The number of ways, in which he can put these books in the bags so that no bag is empty, is :

1. 18
2. 36
3. 39
4. 72

The number of 4-letter words, with or without meaning, each consisting of two vowels and two consonants that can be formed from the letters of the word INCONSEQUENTIAL, without repeating any letter, is :

1. 2670
2. 2840
3. 2920
4. 3600

A building has ground floor and 10 more floors. Nine persons enter in a lift at the ground floor. The lift goes up to the 10th floor. The number of ways, in which any 4 persons exit at a floor and the remaining 5 persons exit at a different floor, if the lift does not stop at the first and the second floors, is equal to :

1. 2184
2. 3064
3. 7056
4. 11340

Two players A and B play a series of games of badminton. The player, who wins 5 games first, wins the series. Assuming that no game ends in a draw, the number of ways, in which player A wins the series is .

A box contains 5 blue, 6 yellow and 4 red balls. The number of ways, of drawing 8 balls containing at least two balls of each colour, is :

1. 4100
2. 4140
3. 4230
4. 4290

The number of ways, of forming a queue of 4 boys and 3 girls such that all the girls are not together, is:

1. 5040
2. 3050
3. 3410
4. 4320

Let A=\(a, b, c) : a, b, c are non-negative integers and a+b+2c=22\. Then n(A) is equal to :

1. 121
2. 124
3. 144
4. 169

The number of seven-digit numbers, that can be formed by using the digits 1, 2, 3, 5 and 7 such that each digit is used at least once, is :

1. 15400
2. 17800
3. 16800
4. 29400

Let pn denote the total number of triangles formed by joining the vertices of an n-side regular polygon. If pn+1-pn=66, then the sum of all distinct prime divisors of n is :

1. 7
2. 8
3. 5
4. 6

Let S = \1, 2, 3, 4, 5, 6, 7, 8, 9\. Let x be the number of 9-digit numbers formed using the digits of the set S such that only one digit is repeated and it is repeated exactly twice. Let y be the number of 9-digit numbers formed using the digits of the set S such that only two digits are repeated and each of these is repeated exactly twice. Then,

1. 56x = 9y
2. 21x = 4y
3. 45x = 7y
4. 29x = 5y

Three persons enter in a lift at the ground floor. The lift will go up to 10th floor. The number of ways, in which the three persons can exit the lift at three different floors, if the lift does not stop at first, second and third floors, is equal to .

The number of numbers greater than 5000, less than 9000 and divisible by 3, that can be formed using the digits 0, 1, 2, 5, 9, if the repetition of the digits is allowed, is

The letters of the word "UDAYPUR" are written in all possible ways with or without meaning and these words are arranged as in a dictionary. The rank of the word "UDAYPUR" is

1. 1579
2. 1578
3. 1580
4. 1581

The largest value of n, for which 40n divides 60!, is

1. 14
2. 13
3. 11
4. 12

The number of 4-letter words, with or without meaning, which can be formed using the letters PQRPQRSTUVP, is .

The number of ways, in which 16 oranges can be distributed to four children such that each child gets at least one orange, is

1. 384
2. 403
3. 429
4. 455

Let S denote the set of 4-digit numbers abcd such that a > b > c > d and P denote the set of 5-digit numbers having product of its digits equal to 20 . Then n(S) + n(P) is equal to

Let ABC be a triangle. Consider four points p1, p2, p3, p4 on the side AB, five points p5, p6, p7, p8, p9 on the side BC, and four points p10, p11, p12, p13 on the side AC. None of these points is a vertex of the triangle ABC. Then the total number of pentagons, that can be formed by taking all the vertices from the points p1, p2, , p13, is

Let S = \(m, n) : m, n \1, 2, 3, , 50\\. If the number of elements (m, n) in S such that 6m + 9n is a multiple of 5 is p and the number of elements (m, n) in S such that m + n is a square of a prime number is q, then p + q is equal to .

The largest n N, for which 7n divides 101!, is :

1. 18
2. 15
3. 19
4. 16

There are 12 points in a plane, no three of which are in the same straight line, except 5 points which are collinear. Then the total number of triangles that can be formed with the vertices at any three of these 12 points is

1. 230
2. 210
3. 200
4. 220

From a group of 7 batsmen and 6 bowlers, 10 players are to be chosen for a team, which should include at least 4 batsmen and at least 4 bowlers. One batsman and one bowler who are captain and vice-captain respectively of the team should be included. Then the total number of ways such a selection can be made, is

1. 145
2. 165
3. 155
4. 135

For n 2, let Sn denote the set of all subsets of \1, 2, , n\ with no two consecutive numbers. For example \1, 3, 5\ S6, but \1, 2, 4\ S6. Then n(S5) is equal to

Let m and n, (m<n), be two 2-digit numbers. Then the total number of pairs (m, n), such that (m, n)=6, is .

All five letter words are made using all the letters A, B, C, D, E and arranged as in an English dictionary with serial numbers. Let the word at serial number n be denoted by Wn. Let the probability P(Wn) of choosing the word Wn satisfy P(Wn) = 2 P(Wn-1), n > 1. If P(CDBEA) = 2 2 -1, , N, then + is equal to

If the number of seven-digit numbers, such that the sum of their digits is even, is m n 10n; m, n \1, 2, 3, , 9\, then m + n is equal to

Line L1 of slope 2 and line L2 of slope 12 intersect at the origin O. In the first quadrant, P1, P2, , P12 are 12 points on line L1 and Q1, Q2, , Q9 are 9 points on line L2. Then the total number of triangles, that can be formed having vertices at three of the 22 points O, P1, P2, , P12, Q1, Q2, , Q9, is:

1. 1026
2. 1188
3. 1134
4. 1080

The largest n N such that 3n divides 50 ! is :

1. 22
2. 20
3. 21
4. 23

The number of sequences of ten terms, whose terms are either 0 or 1 or 2, that contain exactly five 1s and exactly three 2s, is equal to :

1. 360
2. 2520
3. 1820
4. 45

The number of ways, in which the letters A, B, C, D, E can be placed in the 8 boxes of the figure below so that no row remains empty and at most one letter can be placed in a box, is : [figure]

1. 5880
2. 840
3. 960
4. 5760