Question

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

• A. $5$
• B. $21$
• C. ${{}^{8}C}_3$
• D. $3^8$

Answer 1

The correct option is B $21$

The total number of ways of dividing $n$ identical balls in $r$ distinct boxes so that none of the boxes is empty

$={{}^{n-1}C}_{r-1}$

Here we have to distribute 8 identical balls in 3 distinct boxes.

This can be done in ${{}^{8-1}C}_{3-1}={{}^{7}C}_2=\frac{7!}{5!2!}=21$ ways.