If $^nC_{15} = ^nC_8$,then what is the value of $^nC_{21}$?

In how many ways can a committee of $6$ members be formed from $8$ men and $4$ women such that the committee contains at least $3$ women?

There are $12$ volleyball players in total in a college,out of which a team of $9$ players is to be formed. If the captain always remains the same,in how many ways can the team be formed?

To fill $12$ vacancies,there are $25$ candidates,of which $5$ are from the 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 is:

The number of ways to select $n$ objects from $2n$ objects, of which $n$ are identical and the rest are different, is:

The greatest positive integer which divides $(n+16)(n+17)(n+18)(n+19)$,for all positive integers $n$,is