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Thread: Combination Question

  1. #1
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    Combination Question

    Question:
    Ten boxes each hold one white ball and one coloured ball every colour being different. Find the number of ways in which one ball may be taken from each box if half those taken are white.

    10 boxes 10 choices 2 balls in each box but half of them already taken to be white
    so there are 5 boxes left with 2 choices 5C2

    so; 5 x 5C2 = 50
    but the answer in the textbook is 252

    Please help I am having difficult in understanding the question
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  2. #2
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    Re: Combination Question

    first pick the 5 boxes you will choose the white ball from.

    There are $\dbinom{10}{5}=252$ of these

    And that's all the choosing you can do. The other colors are just the ones left in the boxes you didn't choose.
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  3. #3
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    Re: Combination Question

    Quote Originally Posted by bigmansouf View Post
    Question:
    Ten boxes each hold one white ball and one coloured ball every colour being different. Find the number of ways in which one ball may be taken from each box if half those taken are white.

    10 boxes 10 choices 2 balls in each box but half of them already taken to be white
    so there are 5 boxes left with 2 choices 5C2

    so; 5 x 5C2 = 50
    but the answer in the textbook is 252

    Please help I am having difficult in understanding the question
    There 10C5 ways to choose the boxes from which to take the white balls. That also determines the boxes from which to take the colored balls. So your answer is just 10C5.

    Edit: I see Romsek beat me to it...
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