Question

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

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

Answer 1

Answer: (B)

$21$

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

${}^{(8-1)}{C}_{(3-1)}$ [ Using direct formula]

$={}^7{C}_2$

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

$=7\times 3$

$=21$.