Variance to mean ratio of a random intersection

Two subsets $A$ and $B$ of $\{1,2,\dots,20\}$ are chosen independently and uniformly from all $2^{20}$ subsets (they may coincide). With $N=|A\cap B|$, compute $\operatorname{Var}(N)/\mathbb{E}[N]$.

$\tfrac34$. Each element lies in $A$ and in $B$ independently with probability $\tfrac12$ each, so it lies in the intersection with probability $\tfrac14$, independently of other elements. Hence $N\sim\text{Bin}(20,\tfrac14)$ and the ratio is $1-p=\tfrac34$.