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Math Help - Permutation ans combination

  1. #1
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    Permutation ans combination

    1) seven people, of whom four are women and three are men, are to form a queue. find how many different arrangements there are if no two men may stand next to each other.

    these seven people sit at a round table. find the number of ways of arranging them if a particular woman is seated between two men

    2) A painter is given the job of painting the doors of 5 adjacent bedroom using 5 colours, red, bkue, yellow, green and orange

    if the owner of the house insists that the doors should be painted with at most two colours, find the number of ways which the painter could have the job done
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  2. #2
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    Quote Originally Posted by guess
    1) seven people, of whom four are women and three are men, are to form a queue. find how many different arrangements there are if no two men may stand next to each other.

    these seven people sit at a round table. find the number of ways of arranging them if a particular woman is seated between two men
    Notice you possibilites are,
    MWMWMWW
    MWWMWMW
    MWMWWMW
    WMWMWWM
    WMWWMWM
    WWMWMWM
    Each one gives 4!\cdot 3! and there are six thus,
    6\cdot 4!\cdot 3!=6\cdot 24\cdot 6=864
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