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Math Help - Counting - More Generalized Permutations and Combinations

  1. #1
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    Counting - More Generalized Permutations and Combinations

    Problem Statement:
    "A bag contains 20 balls (six red, six green, eight purple). In how many ways can we draw two red, three green, and two purple balls if the ball are considered distinct?"

    Solution:
    Since the balls are considered distinct, there is no repetition allowed.

    C(6,2)*C(6,3)*C(8,2) = 15*20*28 = 8400 ways.

    Is this the correction solution?
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  2. #2
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    Quote Originally Posted by sedemihcra View Post
    Problem Statement:
    "A bag contains 20 balls (six red, six green, eight purple). In how many ways can we draw two red, three green, and two purple balls if the ball are considered distinct?"

    Solution:
    Since the balls are considered distinct, there is no repetition allowed.

    C(6,2)*C(6,3)*C(8,2) = 15*20*28 = 8400 ways.

    Is this the correction solution?
    Dear sedemihcra,

    If you are concerned about the selection order of these balls (i.e: you could select the red ones first green ones second and purple ones third or you can select purple ones first then red ones and green ones etc....)
    then you have to multiply the answer by 3!(three factorial.) Otherwise to my mind your solution is correct.

    Hope this will help you.
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