Question

The number of ways of distiributing $8$ identical balls in three distinct boxes so that none of the boxes is empty

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

Answer 1

The correct option is D $21$

The required number of ways is

$={}^{8-1}{C}_{3-1}$

$={}^7{C}_2$

$=\frac{7\times 6}{2!}$

$=21$

Hence there are in total 21 ways.