Three pairs of women are each married to twin men in such a

Three pairs of women are each married to twin men in such a way that each woman\'s twin sister is married to her husband\'s twin brother. If all twelve of them enter a mixed doubles tennis tournament, in how many ways can they be arranged as six matched pairs so that no one is paired with their spouse or their twin\'s spouse. (In mixed doubles, each team is a pair consisting of one man and one woman, so the question asks how many different teams are possible).

Please explain how you arrived at your answer explicitly, rather than just copy-pasting the answer from some other site. I struggle to understand these kinds of problems. Thank you.

Solution

<p>Three pairs of women are each married to twin men in such a way that each woman\'s twin sister is married to her husband\'s twin brother. If all twelve of them enter a mixed doubles tennis tournament, in how many ways can they be arranged as six matched pairs so that no one is paired with their spouse or their twin\'s spouse. (In mixed doubles, each team is a pair consisting of one man and one woman, so the question asks how many different teams are possible).</p> <p>Please explain how you arrived at your answer&nbsp;<em>explicitly</em>, rather than just copy-pasting the answer from some other site. &nbsp;I struggle to understand these kinds of problems. &nbsp;Thank you.</p>