We have an urn containing $k$ balls where for all $i:1\le i\le k$, the ball $b_i$ has the size $s_i$ that determines its probability to be drawn. For instance, a ball $b_i$ with size $s_i=3$ is three times more likely to be drawn than a ball $b_j$ with size $s_j=1$.
From this urn we draw $n$ times without replacement. What is the expected sum of the sizes of all drawn balls?