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Math Help - Permutations and combinations

  1. #1
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    Permutations and combinations

    There are five members of the Math Club. In how many ways can the positions of officers, a president, and a treasurer, be chosen? I thinked it's just 5 factorial. But the answer is 20. Which means they divided by 3 factorial... Why ?
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  2. #2
    Member kalyanram's Avatar
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    Re: Permutations and combinations

    You have two offices (President, Treasurer). Now you have to choose 2 people from a group of 5 how many ways can this can be done.
    Spoiler:
    In  2.\binom{5}{2} = 2.\frac{5!}{2!3!} = 20 ways. Multiplication by two is to allow permutations among them. Thanks to Evgeny (emakarov) for the correction.
    Last edited by kalyanram; September 14th 2012 at 09:06 AM.
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  3. #3
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    Re: Permutations and combinations

    Quote Originally Posted by Shwems View Post
    There are five members of the Math Club. In how many ways can the positions of officers, a president, and a treasurer, be chosen? I thinked it's just 5 factorial. But the answer is 20. Which means they divided by 3 factorial... Why ?
    See k-permutations.
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