Question

Five balls are to be placed in three boxes. Each box should hold all the five balls so that no box remains empty. Number of ways if balls and boxes are identical is

• A. $3$
• B. $1$
• C. $2$
• D. None of these

Answer 1

Answer: (C)

$2$

As no box is to remain empty boxes can have balls in the following numbers.

Case: $1,1,3$ or $1,2,2$

When balls as well as boxes are identical, the number of combinations and arrangements will be $1$ each in both cares

.

$\therefore$ the required number of ways $=1+1=2$.

Hence option ${}^{\prime }{C}^{\prime }$ is the answer.