Find the number of ways in which `n` different prizes can be distributed among `m(< n)` persons if each is entitled to receive at most `n-1` prizes.

Find the number of ways in which 8 non-identical apples can be distributed among 3 boys such that every boy should get at least 1 apple and at most 4 apples.

The total number of ways in which 5 balls of different colours can be distributed among 3 persons, so that each person gets atleast one ball is

n different toys have to be distributed among n children. Find the number of ways in which these toys can be distributed so that exactly one child gets no toy.

Statement 1: The number of positive integral solutions of a b c=30 is 27. Statement 2: Number of ways in which three prizes can be distributed among three persons is 3^3 (a) Statement 1 and Statement 2 , both are correct. Statement 2 is correct explanation for Statement 1. (b) Statement 1 and Statement 2 , both are correct. Statement 2 is not the correct explanation for Statement 1. (c) Statement 1 is correct but Statement 2 is not correct. (d) Statement 2 is correct but Statement 1 is not correct.

Find the number of ways in which 8 different flowered can be strung to form a garland so that four particular flowers are never separated.

Statement 1: ((n^2)!)/((n !)^n) is natural number of for all n in N Statement 2: Number of ways in which n^2 objects can be distributed among n persons equally is (n^2)!//(n !)^n .

Find the number of ways in which 10 different diamonds can be arranged to make a necklace.

Find the number of ways in which 12 different beads can be arranged to form a necklace.

Find the number of ways in which 22 different books can be given to 5 students, so that two students get 5 books each and all the remaining students get 4 books each.

Statement 1: number of ways in which 10 identical toys can be distributed among three students if each receives at least two toys is .^6C_2 . Statement 2: Number of positive integral solutions of x+y+z+w=7i s^6C_3dot