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Math Help - Past exam questions help

  1. #1
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    Past exam questions help

    Hi,

    There is one question I don't understand.

    A bin contains 5 matched pairs of gloves. Each matched pair contains a left hand and a right hand glove that match. In how many ways can 4 gloves be taken from the bin without including a matched pair?

    Possible answers: 160, 120, 80, 40, 30
    Last edited by smallfry; February 16th 2011 at 03:58 PM.
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  2. #2
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    Quote Originally Posted by smallfry View Post
    Hi,

    My professor posted some past exam questions, but didn't post the answers to them

    Can anyone tell me if my answers are right?

    And for #2, I have no clue what the answer is, so that one is the most important!

    (click it to make it bigger)



    Thanks!
    Too many questions in one thread.
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  3. #3
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    Quote Originally Posted by dwsmith View Post
    Too many questions in one thread.
    Sorry I'm pretty sure about most of them except number 2... I'm gonna edit the thread to contain only it.
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  4. #4
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    Quote Originally Posted by smallfry View Post
    Hi,

    There is one question I don't understand.

    A bin contains 5 matched pairs of gloves. Each matched pair contains a left hand and a right hand glove that match. In how many ways can 4 gloves be taken from the bin without including a matched pair?

    Possible answers: 160, 120, 80, 40, 30
    Since there are 5 pairs of gloves, there are 10 gloves. If you want the number of combinations of 2 gloves you can make from these 10 then you evaluate \displaystyle {10\choose{2}}.

    But since you want the number of combinations without matching pairs, you need to realise that there are 5 matching pairs, so the number of non-matching pairs are

    \displaystyle {10\choose{2}} - 5.
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  5. #5
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    The question says that we choose 4 gloves from 10 though.

    Here's my best answer

    Total ways of choosing 4 from 10:
    \displaystyle {10\choose{4}} = 210

    Number of ways of choosing TWO pairs of gloves (we don't want this):
    \displaystyle {5\choose{2}} = 10

    Number of ways of choosing ONE pair of gloves (we don't want this either):
    \displaystyle {5\choose{1}} * \displaystyle {4\choose{2}} * 2^2 = 130

    Total ways = 210 - 10 - 130 = 80
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  6. #6
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    Quote Originally Posted by smallfry View Post
    The question says that we choose 4 gloves from 10 though.

    Here's my best answer

    Total ways of choosing 4 from 10:
    \displaystyle {10\choose{4}} = 210

    Number of ways of choosing TWO pairs of gloves (we don't want this):
    \displaystyle {5\choose{2}} = 10

    Number of ways of choosing ONE pair of gloves (we don't want this either):
    \displaystyle {5\choose{1}} * \displaystyle {4\choose{2}} * 2^2 = 130

    Total ways = 210 - 10 - 130 = 80
    Grrr, misread the question.
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  7. #7
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    No problem it happens to the best of us. But does that answer make sense?
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