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Math Help - arrangement probability

  1. #1
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    arrangement probability

    hello, this was a multiple choice question.

    The letters P, Q ,R,S,T and U are arranged randomly in a line. what is the probability that P and Q are next to each other.

    A) \frac{2X5!}{6!}

    B) \frac{2X6!}{5!}

    C) \frac{5X2!}{6!}

    D) \frac{5X6!}{2!}

    i think i can eliminate B and D because i would not get a decimal for my answer but am not too sure anyway.
    can someone please show me how this question is solved..
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  2. #2
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    There are 6! permutations of the 6 letters so you know that has to be your denominator.

    If you join the two letters they can be in seats 1&2, 2&3, 3&4, 4&5, or 5&6.

    So there are 5 seat combinations that they can occupy and they can go QP or PQ so I believe the answer is 5!*2! / 6!.

    Answer A.
    Last edited by tedmetro; June 1st 2010 at 08:44 PM. Reason: spelling
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