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Math Help - Permutation or Combination?

  1. #1
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    Permutation or Combination?

    I was wondering if someone could offer some guidance as to whether this problem is a permutation or combination.

    A newcomers' club of 30 people wants to choose an executive board consisting of president, secretary, treasurer, and 2 other officers. In how many ways can this be accomplished?

    To me, it seems as though this would be a permutation because the order of the officers matters because each has a distinct job.
    P(30,5)=(30)(29)(28)(27)(26)=17100720

    I am not sure though. What do you think?
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  2. #2
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    Quote Originally Posted by discretec View Post
    I was wondering if someone could offer some guidance as to whether this problem is a permutation or combination.

    A newcomers' club of 30 people wants to choose an executive board consisting of president, secretary, treasurer, and 2 other officers. In how many ways can this be accomplished?
    Order does matter for three of the positions.
    ^{30}\mathcal{P}_3\cdot ^{27}\mathcal{C}_2.
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  3. #3
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    Quote Originally Posted by Plato View Post
    Order does matter for three of the positions.
    ^{30}\mathcal{P}_3\cdot ^{27}\mathcal{C}_2.
    Thanks, I also thought that could be possible, but was not sure. I appreciate your help.
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