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Math Help - Ways to choose three people from a committe

  1. #1
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    Ways to choose three people from a committe

    Given an eight-person committee, how many ways are there to choose the officer positions (chair person, vice-chairperson, and secretary) if a specific member of the committee (Angie) is either the vice-chairperson or she is not an officer?

    There are a total of P(8, 3) = 8 * 7 * 6 = 336 ways to choose the officers without the last condition. However, given the condition the question has me stumped. Any suggestions?
    Last edited by battery88; February 11th 2013 at 06:59 AM.
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  2. #2
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    Re: Ways to choose three people from a committe

    Quote Originally Posted by battery88 View Post
    Given an eight-person committee, how many ways are there to choose the officer positions (chair person, vice-chairperson, and secretary) if a specific member of the committee (Angie) is either the vice-chairperson or she is not an officer?
    Either she is or she is not.

    \mathcal{P}^7_2+\mathcal{P}^7_3
    Last edited by Plato; February 11th 2013 at 07:02 AM.
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  3. #3
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    Re: Ways to choose three people from a committe

    Hello, battery88!

    We must "talk" our way through this.


    Given an eight-person committee, how many ways are there to choose the officer positions
    (chair person, vice-chairperson, and secretary) if a specific member of the committee (Angie)
    is either the vice-chairperson or she is not an officer?

    It seems that Angie wants to be Vice-chair or nothing at all.
    Very well, consider the two cases.

    (1) Angie is Vice-chairman.
    Then the other two offices (Chair, Secretary) can be filled in: 7\cdot6 \,=\,42 ways.

    (2) Angie is not Vice-chairman. .(Angie is "out of the running".)
    Then the three offices can be filled by the other seven members: 7\cdot6\cdot5 \,=\,210 ways.

    Answer: . 42 + 210 \:=\:210 ways.
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    Re: Ways to choose three people from a committe

    Thanks for the help. I can see it now!
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