Question

The number of ways to give away 20 apples to 3 boys, each boy receiving at least 4 apples, is

• A. ${}^{10}{C}_8$
• B. 90
• C. ${}^{22}{C}_{20}$
• D. none of these

Answer 1

Answer: (A)

${}^{10}{C}_8$

First we give 4 apples to each boy.
Then we are left with exactly 8 apples.
Distribution of 8 apples to 3 boys implies non-negative integral solution of $x+y+z=8$.
That is
${}^{10}{C}_8$.