j_bertolotti<p>Given that I am surrounded by Mathematicians here, let me ask for help for what should be a simple problem I can&#39;t seem to be able to solve:<br />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&lt;k&lt;=n) highest results. What is the probability that the sum of the k dice you kept is X?<br />(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).</p><p><a href="https://mathstodon.xyz/tags/ProbabilityTheory" class="mention hashtag" rel="tag">#<span>ProbabilityTheory</span></a> <a href="https://mathstodon.xyz/tags/IShouldKnowHowToSolveThisButIDoNot" class="mention hashtag" rel="tag">#<span>IShouldKnowHowToSolveThisButIDoNot</span></a> 😞</p>