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Math Help - Five siblings

  1. #1
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    Five siblings

    Five siblings, Paula Mike Stephanie, Kurt and Emily are randomly seated along one side of a long table
    What is the probability that the children are seated
    a) with three girls in the middle
    b) in order of age

    Any help is appreciated
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  2. #2
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    Quote Originally Posted by Runes View Post
    Five siblings, Paula Mike Stephanie, Kurt and Emily are randomly seated along one side of a long table
    What is the probability that the children are seated
    a) with three girls in the middle
    b) in order of age

    Any help is appreciated
    There are five slots:
    X X X X X
    Where one of the kids go into those slots.
    There are 5! = 120 make an arrangement.

    In (a) we want B G G G B there are 3! = 6 to seat the girls in the middle and 2! = 2 ways to seat the boys. Thus there are 6*2 = 12 to make this seating. The probability is 12/120 = 1/10

    In (b) then A B C D E or E D C B A where A is younest and E is largest. There are only 2 ways the probability is 2/120 = 1/60
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