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Math Help - Permutation Question

  1. #1
    Member
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    Question Permutation Question

    I have the answer but how should it be solved ? This way 1P1*1P1*6P6 ?

    Question

    7 boys are seated in a row. Calculate different ways in which this can be done if 2 particular boys A and B have exactly 3 other boys between them.

    Answer

    720
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  2. #2
    MHF Contributor

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    Mar 2011
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    Tejas
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    Re: Permutation Question

    If B is 3 chairs to the right of A, A can only be seated in chair 1,2, or 3. Otherwise, B is to the left of A, and the possible positions of A and B are switched. That gives 6 possible ways to seat A and B:

    A---B--
    -A---B-
    --A---B
    B---A--
    -B---A-
    --B---A

    For each of these ways there are 5! = 120 ways to seat the remaining 5 boys. That gives 6*(5!) = 6! = 720 possible ways to seat the 7 boys under the restrictions listed.
    Thanks from haftakhan
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