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

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Question

(A) Total candidates = $25$. Scheduled caste candidates = $5$. Other candidates = $25 - 5 = 20$.Total vacancies = $12$. Reserved vacancies for schedul

Vedclass · Accepted Answer

$^5C_3 	imes ^{22}C_9$

Vedclass · Answer

(A) Total candidates = $25$. Scheduled caste candidates = $5$. Other candidates = $25 - 5 = 20$.Total vacancies = $12$. Reserved vacancies for scheduled caste = $3$. Open vacancies = $12 - 3 = 9$.Step $1$: Selection for $3$ reserved vacancies from $5$ scheduled caste candidates can be done in $^5C_3$ ways.Step $2$: After filling $3$ reserved seats,the remaining candidates are $25 - 3 = 22$ (since $2$ scheduled caste candidates were not selected for reserved seats,they are now eligible for the open seats along with the $20$ other candidates).Step $3$: The remaining $9$ vacancies are open to all remaining $22$ candidates. This can be done in $^{22}C_9$ ways.Total number of ways = $^5C_3 	imes ^{22}C_9$.

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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