Question

To fill $12$ vacancies there are $25$ candidates of which $5$ are from scheduled castes. $3$ of the vacancies are reserved for scheduled caste candidates while the rest are open for all, the number of ways this selection can be made is

• A. ${}^{20}{C}_9{.}^5{C}_3$
• B. ${}^{25}{C}_{12}$
• C. ${}^{20}{C}_9$
• D. ${}^{20}{C}_5$

Answer 1

The correct option is A ${}^{20}{C}_9{.}^5{C}_3$

There are $5$ SCs and $20$ open we have to choose $3$ SCs and $9$ open${=}^5{C}_3{.}^{20}{C}_9$ ways