Question

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

• A. $10!$
• B. $\frac{10!}{5!}$
• C. $\frac{10!}{{\left(5!\right)}^2}$
• D. None of these

Answer 1

The correct option is C

$\frac{10!}{{\left(5!\right)}^2}$

The explanation for the correct answer.

Find the number of ways:

Given: Total number of boxes are $10$ and the balls are $5$.

Five identical balls are distributed among ten boxes,

$={}^{10}{\mathrm{C}}_5$

$=\frac{10!}{5!\left(10-5\right)!}$

$=\frac{10!}{{\left(5!\right)}^2}$

Hence option $\left(c\right)$ is the correct answer.