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Math Help - circular permutation

  1. #1
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    circular permutation

    hope some body can explain for me for this problem... i already stuck:

    In how many different arrangements can 6 gentlemen and 6 ladies sit around a table if no two ladies sit side by side?

    ans:
    the number of ways in which 6 gentlemen can be seated around a table = (6 - 1)! = 5!.

    Then, corresponding to each seating arrangement for the gentlemen, the 6 ladies can be seated in 6! ways.

    he required number of arrangements = (5!)(6!)

    my opinion is number of ways in which 6 ladies can be seated around a table = 5!.cand not 6!...

    any one can eplane why
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  2. #2
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    Quote Originally Posted by nikk View Post
    In how many different arrangements can 6 gentlemen and 6 ladies sit around a table if no two ladies sit side by side?
    ans:
    the number of ways in which 6 gentlemen can be seated around a table [in every other set] = (6 - 1)! = 5!.
    Then, corresponding to each seating arrangement for the gentlemen, the 6 ladies can be seated in 6! ways.
    he required number of arrangements = (5!)(6!)
    See my addition above.
    Once one person is seated, let alone six, it is no longer circular but becomes linear because we now have right and left.
    So it is 6!
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  3. #3
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    Quote Originally Posted by Plato View Post
    See my addition above.
    Once one person is seated, let alone six, it is no longer circular but becomes linear because we now have right and left.
    So it is 6!
    tq for the explanation, but why 6 ladies can be seated in 6! ..why is not 5! also as per gentlemen??..that my prob

    tq
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  4. #4
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    Quote Originally Posted by nikk View Post
    but why 6 ladies can be seated in 6! ..why is not 5! also as per gentlemen?
    I will try one more time.
    If we had n men to seat, then place one of those at any seat.
    Now we can seat the others in (n-1)! ways because relative to the first man the table is now ordered (we can seat clockwise from his left or counterclockwise from his right). That is the general rule for all circular arrangement. If we use every other seat and we want to seat n women we have n! ways to do it because that is still ordered by the first man seated.
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  5. #5
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    Smile

    Quote Originally Posted by Plato View Post
    If we use every other seat and we want to seat n women we have n! ways to do it because that is still ordered by the first man seated.
    yap but we still consider that the women still sit in round table. for that, the general rule for all circular arrangement for the women still (n-1)!???

    am i right sir?

    i get the question here All about Circular Permutations - TutorVista.com

    thank in advise me
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