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.

Options

A. `(16!)/(4!5!7!)`
B. 4!5!7!
C. `(16!)/(3!5!8!)`
D. none of these

Explanation

Suppose A gets x things, then B gets x+1 and C gets x+3 things.
`:.x+x+1+x+3=16implies4`.
Thus, we have to distribute 16 things to A, B and C in such a way that A gets 4 things, B gets 5 things and C gets 7 things.
Required number of ways `=""^(16)C_(4)xx""^(12)C_(5)xx""^(7)C_(7)=(16!)/(4!5!7!)`