Use
Algorithm::Combinatorics, that's written in XS.
Edit: you can make your problem easier by mapping your multiset/bag into a set first, so that the simpler algorithms can work: A,A,A,A,A,A,A,A,A,A,B,B,… ⤖ A1,A2,A3,A4,A5,A6,A7,A8,A9,A10,B1,B2,…
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