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Let’s say I have a set $U$ containing some values. I randomly distribute these values into $n$ stacks and sort each stack from largest to smallest. Then I take the top $m$ items from each stack to form a set $S$.

What is the probability the largest $k$ values in $U$ are also in $S$? I can see trivially that the probability is $1$ if $m=k$ but that’s as far as I’ve got.

cpiegore
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Cameron Toy
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  • I suspect that in most cases simulation will be fastest. How is the random distribution done (with some methods there is a positive probability there could be some stacks with fewer than $m$ items)? – Henry Apr 22 '23 at 20:25

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