Question

The number of ways of distribution 8 identical balls in 3 distinct boxes so that none of the boxes is empty is

Answer 1

The total no. of ways of dividing $8$ identical balls in $3$ distinct boxes so that none of the boxes is empty is$:$

${}^{\left(8-1\right)}{C}_{3-1}{=}^7{C}_2$

$\Rightarrow \frac{7!}{2!\times 5!}$

$\Rightarrow \frac{7\times 6\times 5!}{2\times 1\times 5!}$

$\Rightarrow 21$

The number of ways $=21.$