Permutations and Combinations

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 .