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Math Help - Arrangement of couples

  1. #1
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    Arrangement 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!
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  2. #2
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    Using inclusion/exclusion \sum\limits_{k = 0}^n {\left( { - 1} \right)^k \binom{n}{k}\left( {2n - k} \right)!\left( {2^k } \right)} .
    Last edited by Plato; October 17th 2009 at 06:27 AM.
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  3. #3
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    Quote Originally Posted by Plato View Post
    Using inclusion/exclusion \sum\limits_{k = 0}^n {\left( { - 1} \right)^k \binom{n}{k}\left( {2n - k} \right)!\left( {2^k } \right)} .
    @ Plato - Hi

    Did you actually workout all the cases - "1,2,3,...,n couple together" and took a compliment or there was an easy way?

    Thanks
    Last edited by Plato; October 17th 2009 at 06:27 AM.
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  4. #4
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    Quote Originally Posted by aman_cc View Post
    Did you actually workout all the cases - "1,2,3,...,n couple together" and took a compliment
    Exactly. I do not know another way.
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