There are 25 candidates for 12 positions,out | vedclass

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(D) The $3$ reserved positions must be filled by the $5$ reserved category candidates,which can be done in $\binom{5}{3}$ ways.After filling the $3$ r

Vedclass · Accepted Answer

$\binom{5}{3} \cdot \binom{22}{9}$

Vedclass · Answer

(D) The $3$ reserved positions must be filled by the $5$ reserved category candidates,which can be done in $\binom{5}{3}$ ways.After filling the $3$ reserved positions,there are $12 - 3 = 9$ positions remaining.The total number of candidates remaining is $25 - 3 = 22$ (since $3$ reserved candidates are already selected,but the remaining $2$ reserved candidates and $20$ open candidates are available for the $9$ open positions).Thus,the $9$ open positions can be filled from the remaining $22$ candidates in $\binom{22}{9}$ ways.The total number of ways for the selection is $\binom{5}{3} \cdot \binom{22}{9}$.

There are $25$ candidates for $12$ positions,out of which $5$ are from the reserved category. If $3$ positions are reserved and the remaining are open,in how many ways can the selection be made?

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