Question

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

• A. $^8C_3$
• B. 21
• C. $3^8$
• D. 5

Answer 1

Answer: (B)

21

Answer 2

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 $= ^{8-1}C_{3-1}= ^{7}C_{2} = \frac{7!}{2!5!}= \frac{7 \times6}{2 \times1} = 21$