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)

We know that the number of ways of distributing n identical items among r persons, when each one of them receives at least one item is ${}^{n-1}{C}_{r-1}$
$\therefore$ The required number of ways
${=}^{8-1}{C}_{3-1}{=}^7{C}_2=\frac{7!}{2!5!}=\frac{7\times 6}{2\times 1}=21$