Permutations and Combinations · Question 14

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 .