If $^{n}C_{8} = ^{n}C_{2}$,find $^{n}C_{2}$.

Let $S_r = \{(x, y, z) : x + y + z = 11, x \geq r, y \geq r, z \geq r, x, y, z, r \in \mathbb{Z}\}$ and $n(S_r)$ represents the number of elements in $S_r$. Then $n(S_2) + n(S_3) + n(S_4) = $

If $\frac{1}{{ }^{5}C_{r}} + \frac{1}{{ }^{6}C_{r}} = \frac{1}{{ }^{4}C_{r}},$ then the value of $r$ is

The value of ${ }^{16} C_{9}+{ }^{16} C_{10}-{ }^{16} C_{6}-{ }^{16} C_{7}$ is

The number of elements in the set $\{x \in N : ^{20-2x}C_{x-3} \in N\}$ is

$A$ team of $11$ players is to be selected from $22$ players. If $2$ specific players must be included in every team and $4$ specific players must always be excluded,in how many ways can this selection be made?