Ohh does anyone know that other question about "How many ways can a mixed doubles tennis match be played with 6 married couples, so that no husband and wife play in the same match?"
What's to say that there isn't any same-sex marriage involved =)
There are 4 positions in a doubles tennis match.
First position could be anybody of the 12 (6 married couples = 12 people), so we have 12 choices.
Second position could be anybody EXCEPT their partner, so we have 10 choices. (Total 24 - 1 married couple = 10)
Third position could be anybody except the second and first person's partner, so we have 8 choices. (Total - 2 married couples = 8)
Fourth position could be anybody except the first, second and third person's partner, so we have 6 choices. (Total - 3 married couples = 6)
So therefore the number of mixed doubles tennis matches, such that there are no PARTNERS in the same match, is 12 x 10 x 8 x 6 = 5670.