If $^{10}C_r = ^{10}C_{r+2}$,then $^5C_r$ equals

$A$ committee of $4$ members is to be formed from $4$ couples (husbands and wives). In how many ways can the committee be formed such that no couple is included in the committee?

$A$ committee of $7$ members is to be formed from $9$ boys and $4$ girls. In how many ways can this be done if the committee must consist of exactly $3$ girls?

If $\frac{{}^{n+1}C_{r+1}}{{}^{n+1}C_r} = \frac{n-r+1}{m}$,then $m =$

The number of ways in which a team of $11$ players can be formed out of $25$ players,if $6$ out of them are always to be included and $5$ of them are always to be excluded,is

$A$ man has $7$ friends. In how many ways can he invite one or more of them for a tea party?