Question

The number of ways in which five identical balls can be distributed among ten distinct boxes such that no box contains more than one ball, is

• A. 10!
• B. $\frac{10!}{5!}$
• C. $\frac{10!}{{(5!)}^2}$
• D. 1

Answer 1

The correct option is C $\frac{10!}{{(5!)}^2}$

We have, 10 distinct boxes and 5 identical balls. Since, box contain not more than one ball.
Hence, Five balls can be distributed in 10 boxes
Number of ways of distributing balls ${=}^{10}{C}_5=\frac{10!}{5!5!}=\frac{10!}{(5!{)}^2}$