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?

There are $10$ intermediate stations on a railway line between two particular stations. The number of ways that a train can be made to stop at $3$ of these intermediate stations so that no two of these halting stations are consecutive is:

If a committee consists of $3$ men and $2$ women,in how many ways can a committee of $5$ members be formed from $5$ men and $4$ women?

$A$ team of $11$ players is to be selected from $22$ players. If $2$ specific players must be included in every team and $4$ specific players must always be excluded,in how many ways can this selection be made?

The number of integers between $100$ and $1000$ such that the sum of their digits is equal to $14$ is:

If $^nC_r = 84$,$^nC_{r-1} = 36$,and $^nC_{r+1} = 126$,then $n$ equals