Sorry for any bad terminology, that's probably why I can't find info on it.
Let's say I have following multisets (all of the same cardinality):
[red, green, green, yellow] [square, circle, circle, circle] [small, medium, large, large]
I produce a multiset of combinations, according to those rules:
- Each combination consists of items from all those multisets
- From each set, each item is only used once
- The multisets must be fully exhausted (so the cardinality of result multiset = cardinality of original multisets)
So a result multiset of combinations is something like
[red-circle-medium, green-circle-large, green-square-small, yellow-circle-large]
Given that, how do I count the number of distinct result multisets?