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Math Help - hat problem

  1. #1
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    hat problem

    5 people go to a movie theathre. They consign their hats to a cloakroom. What is the probability that when they leaved the theathre 2 of them got their hats?
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  2. #2
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    Re: hat problem

    Quote Originally Posted by kastamonu View Post
    5 people go to a movie theathre. They consign their hats to a cloakroom. What is the probability that when they leaved the theathre 2 of them got their hats?
    Read the article.

    your answer is {5 choose 2}*{derangement of three}
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  3. #3
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    Re: hat problem

    Hello, kastamonu!

    Five people go to a movie theatre and consign their hats to a cloakroom.
    What is the probability that when they leave the theatre, exactly 2 of them got their hats?

    Assuming that the hats are returned randomly,
    . . there are 5! = 120 possible outcomes.

    Call the people A,B,C,D,E.

    First, choose the two people who get their hats.
    . . There are: . {5\choose2} = 10 choices.

    Suppose they are A and B.
    Then C,D,E do not get their hats.
    There are 2 choices: . DEC and ECD.

    Hence, there are: . 10\cdot2 \,=\,20 ways.

    The probability is: . \frac{20}{120} \,=\,\frac{1}{6}
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  4. #4
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    Re: hat problem

    many thanks.
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