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Thread: 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 $\displaystyle 5! = 120$ possible outcomes.

    Call the people $\displaystyle A,B,C,D,E.$

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

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

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

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

    many thanks.
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