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Thread: Circular table permutations problem

  1. #1
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    Circular table permutations problem

    Hey, i have problem understanding how to get result for circular permutations where i have repeating elements.
    I have 10 people in circle, 3 man and 7 women. How can i get number of permutations?

    Result in book is 36.
    I tried
    (9!/2!+7!)+(9!/3!+6!)=120 which is wrong.
    Last edited by PJani; May 11th 2013 at 08:02 AM.
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  2. #2
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    Re: Circular table permutations problem

    Quote Originally Posted by PJani View Post
    Hey, i have problem understanding how to get result for circular permutations where i have repeating elements. I have 10 people in circle, 3 man and 7 women. How can i get number of permutations?

    Result in book is 36.
    That problem as you have posted it is absolutely incomplete.

    As stated the answer is simply $\displaystyle 9!$.

    There must be many more conditions placed on the groups of men and women.

    Please add in those further conditions. That is the only way the answer $\displaystyle 36$ makes any sense.
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  3. #3
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    Re: Circular table permutations problem

    Heh sory, my mistake!
    How can i get number of permutations where i distinguish persons only by gender?
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  4. #4
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    Re: Circular table permutations problem

    Quote Originally Posted by PJani View Post
    Heh sory, my mistake!
    How can i get number of permutations where i distinguish persons only by gender?
    In the future, please try to be clear and complete.

    Place a female anywhere at the table.
    Now you have a string $\displaystyle ffmmmmmmm$ to arrange: $\displaystyle \frac{9!}{2!\cdot 7!}=?$ ways.

    Start at the seated female's right and seat each of those strings counter-clockwise.
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  5. #5
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    Re: Circular table permutations problem

    Why do you start with females? And why is $\displaystyle \frac{9!}{2!\cdot 7!}=?$ and not $\displaystyle \frac{9!}{3!\cdot 6!}=?$
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