Question

To fill $12$ vacancies there are $25$ candidates of which five are from scheduled caste. If $3$ of the vacancies are reserved for scheduled caste candidates while the rest are open to all, then the number of ways in which the selection can be made?

• A. ${}^{5}C_3\times {}^{22}C_9$
• B. ${}^{22}C_9-{}^{5}C_3$
• C. ${}^{22}C_9+{}^{5}C_3$
• D. None of these

Answer 1

The correct option is A

${}^{5}C_3\times {}^{22}C_9$

Explanation for the correct option:

Find the total number of ways in which selection can be done.

It is given that, there are $25$ candidates out of which five are from scheduled caste to fill $12$ vacancies and out of $12$ vacancies $3$ vacancies are reserved for scheduled caste.

So, the number of ways in which three reserved vacancies can be filled are ${}^{5}C_3$.

Now, there are $22$ candidates and $9$ vacancies are left.

So, the number of ways in which we can select $9$ candidates out of $22$ can be given by ${}^{22}C_9$.

Therefore, The total number of ways in which selection can be done are ${}^{5}C_3\times {}^{22}C_9$.

Hence, option $A$ is the correct option.