2n objects of each of three kinds are given to two persons, so that each person gets 3n objects. Prove that this can be done in `3n^2 + 2n + 1 ` ways .

In how many ways can n things be given to p persons, when each person can get any number of things.

5 different objects are to be distributed among 3 persons such that no two persons get the same number of objects. Number of ways this can be done is,

The number of ways in which 2n objects of one type, 2n of another type and 2n of a third type can be divided between 2 persons so that each may have 3n objects is alpha n^(2)+beta n +gamma . Find the value of (alpha+beta+gamma) .

Find the number of ways of disturbing n identicalobjects among n persons if at least n-3 persons get none of these objects.

The number of ways of distributing 12 different objects among three person such that one particular person is always getting 6 objects and the remaining two persons are getting three objects each is

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

If N denotes the number of ways of selecting r objects of out of n distinct objects (rgeqn) with unlimited repetition but with each object included at least once in selection, then N is equal is a. .^(r-1)C_(r-n) b. .^(r-1)C_n c. .^(r-1)C_(n-1) d. none of these

Which of the following is not the number of ways of selecting n objects from 2n objects of which n objects are identical

If n objects are arrange in a row, then the number of ways of selecting three of these objects so that no two of them are next to each other is a. "^(n-2)C_3 b. "^(n-3)C_2 c. "^(n-3)C_3 d. none of these

If n objects are arrange in a row, then the number of ways of selecting three of these objects so that no two of them are next to each other is