Question

Find the number of ways to give 16 different things to three persons A, B, C so that B gets 1 more than A and C gets 2 more than B.

Answer 1

Let A get n objects, then B gets n+1 and C gets n+3
Now `n+n+1+n+3=16 implies n=4`
Thus, A, B, C get 4,5 and 7 objects respectively.
Hence, number of ways of distribution is equal to the number of ways 16 objects can be divided into three groups of size 4, 5 and 7.
`therefore " Number of ways" =(16!)/(4!5!7!)`.