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Math Help - Confused about combinations

  1. #1
    Member Rimas's Avatar
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    Confused about combinations

    There are 100 members in the U.s. Senate(2 from each state)In how many ways can a committee of 5 senators be formed if no state may be represened more than once.

    I think that this a permutation problem but when i re-read it it might be a combination problem
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  2. #2
    Senior Member OReilly's Avatar
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    Quote Originally Posted by Rimas View Post
    There are 100 members in the U.s. Senate(2 from each state)In how many ways can a committee of 5 senators be formed if no state may be represented more than once.

    I think that this a permutation problem but when i re-read it it might be a combination problem
    50 senators may form committee in (50*49*48*47*46) / 5! = 2118760 ways.

    Knowing that there 100 senators, multiply that number with 2 and you will get total ways of combinations of committee.
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  3. #3
    MHF Contributor Quick's Avatar
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    Quote Originally Posted by OReilly View Post
    50 senators may form committee in (50*49*48*47*46) / 5! = 2118760 ways.

    Knowing that there 100 senators, multiply that number with 2 and you will get total ways of combinations of committee.
    I don't agree. Let's say there are only 2 states with 2 senators forming a two man comittee.

    Senators a and b are from state "whocares"

    Senators x and y are from state "Ido"

    the combinations with half the senators are:

    ax

    Multiply that by 2 and you get 2 different combinations, and yet possible combinations are:

    ax
    ay
    bx
    by

    it's an unfortunate trick of the problem
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  4. #4
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    Quote Originally Posted by Rimas View Post
    There are 100 members in the U.s. Senate(2 from each state)In how many ways can a committee of 5 senators be formed if no state may be represened more than once.
    There are combin(50,5) to chose the states.
    There are 2^5 ways the chose the members.
    There are combin(50,5)*2^5 ways to do this: 39200 ways.
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