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    ROLCAM's Avatar
    ROLCAM Posts: 1,420, Reputation: 23
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    #1

    Mar 1, 2009, 12:50 AM
    Probabilities ?
    Ten people, all wearing hats, were walking along a street when a sudden wind blew their hats off. A helpful boy retrieved them and, without asking which hat belonged to which person, handed each person a hat. What is the probability that exactly 9 of the people received their own hats?
    galactus's Avatar
    galactus Posts: 2,271, Reputation: 282
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    #2

    Mar 1, 2009, 07:09 AM
    This is what is known as a derangement.

    Think about it. If exactly 9 of the 10 get their own hats, then the 10th must also get his own hat. It's the only one left.

    Its derivation is rather complicated, but the probability that exactly k of N men get their hats back is

    The probability none get their hat back is works out to be 1/e.

    THEREFORE, THE PROB. THAT EXACTLY 9 GE THEIR WON HATS IS 0. Because if 9 get theirs, 10 must get theirs.

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