In how many ways can a team of $3$ boys and $3$ girls be selected from $5$ boys and $4$ girls?

The number of $5$ card combinations out of a deck of $52$ cards such that there is exactly one ace in each combination is:

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

$A$ student is allowed to select at most $n$ books from a collection of $(2n + 1)$ books. If the total number of ways in which he can select at least one book is $63$,then the value of $n$ is

Out of $13$ cricket players,$4$ are bowlers. In how many ways can a team of $11$ players be selected such that the team contains at least $2$ bowlers?

The number of ways to distribute $25$ identical apples among $4$ boys,such that each boy receives at least $4$ apples,is