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

The value of $r$ for which $^{15}C_{r+3} = ^{15}C_{2r-6}$ is

$A$ student is allowed to select at most $n$ books from a collection of $(2n+1)$ books. If the total number of ways in which one can select at least one book is $255$,then the value of $n$ is

If $^{n^2 - n}C_2 = ^{n^2 - n}C_{10}$,then $n = $

If ${ }^{n} C_{12}={ }^{n} C_{8}$,then $n$ is equal to

There are $25$ candidates for $12$ positions,out of which $5$ are from the reserved category. If $3$ positions are reserved and the remaining are open,in how many ways can the selection be made?