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