Let $A$ be the group of whole numbers in the range $[0, n)$. We choose uniformly at random from all subsets of size $k$ ($0 < k < n$).
The mean of the sum of the subset is $\frac{n-1}{2} k$. What is the variance of the sum?
(In fact, I need the variance of the average of the subset, but given the variance of the sum it is easy to calculate)