To fill 12 vacancies,there are 25 candidates, | vedclass

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Question

(A) The selection process is divided into two parts:$1$. Selecting $3$ candidates for the reserved vacancies from the $5$ scheduled caste candidates.

Vedclass · Accepted Answer

$^5C_3 	imes ^{22}C_9$

Vedclass · Answer

(A) The selection process is divided into two parts:$1$. Selecting $3$ candidates for the reserved vacancies from the $5$ scheduled caste candidates. This can be done in $^5C_3$ ways.$2$. After filling the reserved seats,we have $25 - 3 = 22$ candidates remaining (including the $2$ unselected scheduled caste candidates and $20$ others) and $12 - 3 = 9$ vacancies remaining. These $9$ vacancies are open to all remaining $22$ candidates. This can be done in $^{22}C_9$ ways.Therefore,the total number of ways to make the selection is $^5C_3 	imes ^{22}C_9$.

To fill $12$ vacancies,there are $25$ candidates,of which $5$ are from the 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 is:

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