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6.Permutation and Combination
medium
To fill $12$ vacancies there are $25$ candidates of which five are from 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
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
Solution
(a) The selection can be made in $^5{C_3}{ \times ^{22}}{C_9}$.
{Since $3$ vacancies filled from $5$ candidates in $^5{C_3}$ ways and now remaining
candidates are $22$ and remaining seats are $9$}.
Standard 11
Mathematics
