Expected Value for summing over distinct random integers? Let $L=\{a_1,a_2,\ldots,a_k\}$ be a random (uniformly chosen) subset of length $k$ of the numbers $\{1,2,\ldots,n\}$. I want to find $E(X)$ where $X$ is the random variable that sums all numbers. We might want that $k < n$ too.
My main problem is that I cannot get the function $q(a,k,n)$ that gives me the number of ways to write the number $a$ as the sum of exactly $k$ distinct addends less or equal $n$. This seems related but it doesn't limit the size of the numbers.

Hint: (1) Compute $E(a_1)$. (2) Show that $E(a_k)=E(a_1)$ for every $k$. (3) Deduce $E(X)$.
This is a good example where computing the distribution is messy but computing the expectation is easy.
