Question

# To fill up $$12$$ vacancies, there are $$25$$ candidates of which $$5$$ are from SC. If $$3$$ of these vacancies are reserved for SC candidates while the remaining are open to all then the number of ways in which the selection can be made is :

A
5C2×22C13
B
5C3×22C9
C
5C3×23C8
D
8C5×21C7

Solution

## The correct options are A $$^5C_2\times ^{22}C_{13}$$ B $$^5C_3\times ^{22}C_{9}$$$$3$$ vacancies for SC candidates can be filled up from $$5$$ candidates in $$^5C_3$$ ways.After this for remaining $$12-3=9$$ vacancies, there will be $$25-3=22$$ candidates. These vacancies can be filled up in $$^{22}C_9$$ ways. Hence, the required number of ways are $$^5C_3\times {}^{22}C_9$$$$={}^5C_3\times {}^{22}C_9={}^5C_{5-3}\times ^{22}C_{22-9}={}^5C_2\times {}^{22}C_{13}$$Maths

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