Out of $14$ cricket players,$5$ are bowlers. In how many ways can a team of $11$ players be selected such that the team contains at least $4$ bowlers?

The number of ways of selecting a committee of $30$ persons from $20$ boys,$20$ girls,and $20$ teachers such that the participation of the number of boys,girls,and teachers in that committee is equal,is

Determine the number of $5$ card combinations out of a deck of $52$ cards if there is exactly one ace in each combination.

$A$ student is required to answer $10$ questions out of $13$ in an examination,such that he must choose at least $4$ questions from the first $5$ questions. How many ways can he make the selection?

If ${}^nC_{r-1}=330$,${}^nC_r=462$,and ${}^nC_{r+1}=462$,then $r$ is equal to

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?