Given that I am surrounded by Mathematicians here, let me ask for help for what should be a simple problem I can't seem to be able to solve:
Assume you have n fair dice with m faces (i.e. each can roll an integer from 1 to m with a uniform probability). You roll all n, and keep the k (with 0<k<=n) highest results. What is the probability that the sum of the k dice you kept is X?
(If one keeps all the dice, probability-generating functions give the answer straightforwardly. If I roll 2 dice and keep 1 I can easily enumerate the outcomes and calculate the probabilities, but I am stumped by the general case).
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