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

Consider a class of $5$ girls and $7$ boys. The number of different teams consisting of $2$ girls and $3$ boys that can be formed from this class,if there are two specific boys $A$ and $B$ who refuse to be members of the same team,is

If $\binom{15}{3r} = \binom{15}{r+3}$,then $r = \dots$

The least value of $n$ such that ${ }^{(n-1)} C_3 + { }^{(n-1)} C_4 > { }^n C_3$ is:

If $\binom{a^2+a}{3} = \binom{a^2+a}{9}$,then $a = \dots$

If $\binom{n-1}{r} = (k^2 - 3) \binom{n}{r+1}$,then $k \in \dots$