Question

The number of ways in which $5$ identical balls can be kept in $10$ identical boxes. If not more than one can go into a box is?

• A. ${}^{10}P_5$
• B. ${}^{10}C_5$
• C. $5$
• D. $1$

Answer 1

The correct option is B

${}^{10}C_5$

Explanation for the correct option:

Find the required number of combinations.

We have to keep $5$ identical balls in $10$ identical boxes such that no box keep more than one ball.

So, the total number of ways of selecting $5$ boxes from $10$ boxes is ${}^{10}C_5$.

Therefore, The number of ways in which $5$ identical balls can be kept in $10$ identical boxes. If not more than one can go into a box is ${}^{10}C_5$.

Hence, option $B$ is the correct answer.