1. The problem statement, all variables and given/known data I have n balls and m urns numbered 1 to m. Each ball is placed randomly and independently into one of the urns. Let Xi be the number of balls in urn number i. So X1+....+Xm = n What is the distribution of each Xi? What is EXi and VarXi What is E[XiXj] given i≠j What is Cov(X1,Xj? 2. Relevant equations Cov(XY)=Exy(XY)-Ex(X)Ey(Y) 3. The attempt at a solution I read: https://www.artofproblemsolving.com/wiki/index.php?title=Distinguishability and identified this as the last case. I understand that there (n+m-1)ℂ(m-1) ways to place the balls but not how to describe this in the form of a pdf so that I can find expectation and variance and such.