Consider a set of 64 elements exhausted by subsets that have cardinalities 1, 1, 2, 5, 5, 10,10,10,20.
1) How many different ways are there to gather these subsets into two new subsets with 32 elements each?
2) Is this a specific example of a "standard" general problem in combinatorics/combinations that is solved by a "standard" general technique?
3) If so, can you describe or provide a link to the technique?
4) In this case the subset cardinalities have an obvious triplet structure:
1+1 = 2
5+5 = 10
10+10 = 20
Is this particular triplet subset cardinality structure an example of any more general kind of triplet subset cardinality structure that has been previously studied?
Thanks as always for whatever time you can afford to spend considering this matter.