Permutations and Combinations

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