[math-fun] Expected time to get any of several hits

I've been fiddling with the recursion for the expected number of probes [without replacement] to find any of M specific values among N objects. When M=1 the recursion is simple enough: E(N) = 1/N + (N-1)/N * (1+E(N-1))) and it reduces fairly easily to E(N) = (N+1)/2. But for general M it seems a lot harder. The recursion I have is: Em(N) = m/N + (N-m)/N * (1 + Em(N-1)) And I can't see how to simplify it. Am I missing something obvious, or some trick, or is this just a hard one? Thanks!! /bernie\ -- Bernie Cosell Fantasy Farm Fibers mailto:bernie@fantasyfarm.com Pearisburg, VA --> Too many people, too few sheep <--