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Math Help - Probability...i Think nCR

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    Probability...i Think nCR

    Eight kids, 4 boys, 4 girls arrange themselves at random around a merry go round. What is the probabilty that they will be seated alternately.....?

    i cant figure out how to do it...8! ways they could be arranged...but order matters (girls boys) but not between girls and between boys..so how do i do it?
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  2. #2
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    Quote Originally Posted by stones44 View Post
    Eight kids, 4 boys, 4 girls arrange themselves at random around a merry go round. What is the probabilty that they will be seated alternately.....?
    This is a circular arrangement problem. N individuals can be arranged in a circle in (N-1)! Ways.
    So there are (7!) ways to arrange the children.
    Now place the girls in every other set: (3!) ways to do that.
    But now the seats on the ride are ordered, so there are (4!) ways to seat the boys.
    What is the answer?
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    ok so its 4!3! / 7! thanks!....
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    bridge hands

    new thread

    a bridge hand which contains no card higher than a 9 is called a yarborough. what is the probability that one sucj hand will appear in a deal consisting of four hands. what is the probability that two will appear in adeal.
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  5. #5
    Kai
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    Quote Originally Posted by bjhopper View Post
    new thread

    a bridge hand which contains no card higher than a 9 is called a yarborough. what is the probability that one sucj hand will appear in a deal consisting of four hands. what is the probability that two will appear in adeal.
    Hmm, be more specific ? u say cards, is it a pack of unbiased cards of play ?
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  6. #6
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    bridge hands- clarification

    bridge is played with a standard deck of 52 cards. i assume you know the suits and faces
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  7. #7
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    (N-1)! confirmation

    Quote Originally Posted by Plato View Post
    This is a circular arrangement problem. N individuals can be arranged in a circle in (N-1)! Ways.
    So there are (7!) ways to arrange the children.
    Now place the girls in every other set: (3!) ways to do that.
    But now the seats on the ride are ordered, so there are (4!) ways to seat the boys.
    What is the answer?
    So N-1 is because there are N! - N ways in which they can be seated with the same order????
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