There is a set A containing $N$ elements. Then we randomly choose $M$ out of $N (N≥M)$ elements to form a subset B and get the objective function $f(B)$. Different $B$ may lead to different $f(B)$.
My question is how can we get the distribution of $f(B)$? Or is there any paper discussing the relation or the gap between the average value $E[f(B)]$ of $f(B)$ and the optimal value OPT[$f(B)$] of $f(B)$?
Thanks in advance.