I’m struggling to phrase this as a lot as I’m in calculating it.

Alice
Bob
Carol
Dan

All of the combos of their teams, are 15, since I’ve Four singles, 6 doubles, Four triples and 1 quad.
I care about their order, so my whole is definitely 32, since I’ve Four singles, 12 doubles, 12 triples and Four quads.

The maths for this half, I’ve up to now is (earlier than optimizing):

${4choose 1}*1+{4choose 2}*2+{4choose 3}*3+{4choose 4}+4=32$

I’m in search of the best way to generate a pair of pairs, i.e.:

Alice + Bob with Carol + Dan
Alice + Carol with Bob + Dan
Alice + Dan with Bob + Carol

In these, the order doesn’t matter. The entire needs to be Three new combos, however since every has a permutation, every has a results of Four permutations, so one other 12 whole.

The entire right here for a case of Four folks, are 44 potential teams, which embody double pairs.

The right way to I get the full for five folks / X folks?