If $^nC_{15} = ^nC_8$,then what is the value of $^nC_{21}$?

If $x, y$ and $r$ are positive integers,then $^x{C_r} + ^x{C_{r-1}} ^y{C_1} + ^x{C_{r-2}} ^y{C_2} + \dots + ^y{C_r} = $

$A$ boy needs to select five courses from $12$ available courses,out of which $5$ courses are language courses. If he can choose at most two language courses,then the number of ways he can choose five courses is

If $^{n-1}C_r = (k^2 - 3) \cdot ^nC_{r+1}$,then an interval containing the values of $k$ is

In an election,$3$ members are to be elected from $6$ candidates. $A$ voter can cast their vote for any number of candidates but not more than the number of candidates to be elected. In how many ways can a voter cast their vote?

In a library,there are $n$ distinct books and each has $p$ copies. What is the number of ways to select one or more books?