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Math Help - Easy Counting Method Problem

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    Super Member Aryth's Avatar
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    Easy Counting Method Problem

    I've never really been good at choosing the right method, but here's the problem:

    AnnMarie, Beau, Carlos and Dean are four senators on a certain subcommittee. Any or none of them may be selected to another subcommittee. How many different variations for the subcommittee are there?
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    Super Member TheChaz's Avatar
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    Quote Originally Posted by Aryth View Post
    I've never really been good at choosing the right method, but here's the problem:

    AnnMarie, Beau, Carlos and Dean are four senators on a certain subcommittee. Any or none of them may be selected to another subcommittee. How many different variations for the subcommittee are there?
    For A, we have two options: in or out.
    For B, we have two options:
    For C, we have
    For D,

    What can we conclude?
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  3. #3
    MHF Contributor alexmahone's Avatar
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    Quote Originally Posted by aryth View Post
    i've never really been good at choosing the right method, but here's the problem:

    Annmarie, beau, carlos and dean are four senators on a certain subcommittee. Any or none of them may be selected to another subcommittee. How many different variations for the subcommittee are there?
    ^4c_0+^4c_1+^4c_2+^4c_3+^4c_4
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    Super Member Aryth's Avatar
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    Quote Originally Posted by TheChaz View Post
    For A, we have two options: in or out.
    For B, we have two options:
    For C, we have
    For D,

    What can we conclude?
    2^4?

    Quote Originally Posted by alexmahone View Post
    ^4c_0+^4c_1+^4c_2+^4c_3+^4c_4
    Are you suggesting combinations? That's an odd format.... I'm used to _4 C _0... etc.
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    MHF Contributor alexmahone's Avatar
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    Quote Originally Posted by Aryth View Post
    Are you suggesting combinations? That's an odd format.... I'm used to _4 C _0... etc.
    Yes; LaTeX is a little flaky at the moment.

    Note that you get the answer 16 either way.
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    Quote Originally Posted by Aryth View Post
    AnnMarie, Beau, Carlos and Dean are four senators on a certain subcommittee. Any or none of them may be selected to another subcommittee. How many different variations for the subcommittee are there?
    This is a comment on the other correct replies.
    The number of subsets of a set on n elements is \sum\limits_{k = 0}^n \binom{n}{k} =2^n.

    Note that 2^4=16
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