Question

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

• A. ${}^5{C}_3{\times }^{22}{C}_9$
• B. ${}^{22}{C}_9{-}^5{C}_3$
• C. ${}^{22}{C}_3{+}^5{C}_3$
• D. None of these

Answer 1

Answer: (A)

${}^5{C}_3{\times }^{22}{C}_9$

There are 20 open and 5 SC candidates

$3$ SC candidates (out of $5$) can be selected in ${}^5{C}_3$ ways

and remaining $9$ candidates (out of remaining $20+2SC$) can be selected in ${}^{22}{C}_9$ ways.

Therefore, the total ways are $={}^5{C}_3{\times }^{22}{C}_9$