Originally Posted by

**romsek** Ice hockey has 6 people per team, Field hockey has 11 people per team.

Given the wording of the question, i.e. "*the* two teams", I think they are referring to field hockey. This would use all the people mentioned.

A team then must be comprised of 5 couples and 1 spinster. Otherwise some couple would be playing against each other.

given this the answer should be simply

$N = \dbinom{10}{5}\cdot \dbinom{2}{1} = 504$

This is precisely double the answer given. I can't account for the discrepancy. I think it quite possible the answer given is wrong.