If I understand you well, I think a selection of items from a set where the selection order is irrelevant is called a combination. See https://en.wikipedia.org/wiki/Combination. Note that combinations can be with or without repetitions.

Perhaps using this term might help you searching the Internet for algorithms.

In reply to Re^5: Faster alternative to Math::Combinatorics by Laurent_R
in thread Faster alternative to Math::Combinatorics by AppleFritter

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