In how many ways can a team of $11$ players be formed out of $25$ players,if $6$ out of them are always to be included and $5$ are always to be excluded?

From a group of $10$ men and $8$ women,the number of ways of forming a committee of $8$ members with not more than $5$ men and not less than $5$ women is

If ${ }^{11} C_4+{ }^{11} C_5+{ }^{12} C_6+{ }^{13} C_7={ }^{14} C_{r}$,then the value of $r$ is

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?

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

$A$ team of $5$ students is to be selected from $12$ students. If two particular students are to be included in that team,then the number of ways that such team can be selected is