Q:
We have n bins, each bin can store a group of 3 different elements.
in all groups $S \subseteq \{1,\dots, m\}$, $| S|=3$ $$ X_{i,j,k} = \begin{cases} 1, & \text{if i,j,k are in the same bin} \\ 0, & \text{else} \end{cases} $$ $$ X=\sum X_{i,j,k} $$ calculate var$(X)$.
A:
I realize that:
$E(X)={m \choose 3}\frac{1} {n^2}$,
var$(\sum X_{i,j,k}$)=${m \choose 3}\frac{1} {n^2}(1-\frac{1}{n^2})$.
because $X\sim B\left({m \choose 3},\frac{1} {n^2}\right)$
I can't figure out how to tackle the Covariance..