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?

If at the end of a certain meeting,everyone had shaken hands with everyone else,and it was found that $45$ handshakes were exchanged,then the number of members present at the meeting is:

The product of any $r$ consecutive natural numbers is always divisible by

An examiner can assign $30$ marks to $8$ questions. If he does not assign less than $2$ marks to any question,in how many ways can he assign the marks?

In how many ways can a committee of $5$ members be formed from $6$ men and $4$ women such that the committee contains at least one woman?

$^{2n}C_4 : ^nC_3 = 99 : 4 \Rightarrow n = $