How many ways are there to seat n married couples in a row of 2n chairs such that the couples never sit next to each other?

Shouldnt it be as as simple as n.C.2n divided by 2!

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- Oct 17th 2009, 12:52 AMDeRSeDArrangement of couples
How many ways are there to seat n married couples in a row of 2n chairs such that the couples never sit next to each other?

Shouldnt it be as as simple as n.C.2n divided by 2! - Oct 17th 2009, 04:17 AMPlato
Using inclusion/exclusion $\displaystyle \sum\limits_{k = 0}^n {\left( { - 1} \right)^k \binom{n}{k}\left( {2n - k} \right)!\left( {2^k } \right)} $.

- Oct 17th 2009, 05:42 AMaman_cc
- Oct 17th 2009, 05:58 AMPlato