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Math Help - Arrange 248 people in pairs

  1. #1
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    Arrange 248 people in pairs

    1. There are 248 students in a class. In how many ways is it possible to pair the students, in two and two in a pair ?


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  2. #2
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    Re: Arrange 248 people in pairs

    Quote Originally Posted by frimanns View Post
    There are 248 students in a class. In how many ways is it possible to pair the students, in two and two in a pair
    Here is the basic idea.
    Use the first person on the class roll, how many ways can you pick his or her partner?
    Repeat the idea again and again until done.
    \prod\limits_{k = 0}^{123} {(247 - 2k)} that is the same as \frac{248!}{2^{124}(124!)}
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