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Math Help - Pick 6; Match 4

  1. #1
    Member oldguynewstudent's Avatar
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    Pick 6; Match 4

    Just needed somebody to verify this

    In the pick-6 lottery involving the numbers 1-40, you win the Match-4 prize if exactly four of your six numbers appear on the winning ticket. In a given lottery drawing, how many different tickets would win the Match-4 prize?

    \left(\left({6\atop 4}\right)\right) = \left({6+4-1\atop 4}\right) = 126

    Thanks
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  2. #2
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    Quote Originally Posted by oldguynewstudent View Post
    Just needed somebody to verify this

    In the pick-6 lottery involving the numbers 1-40, you win the Match-4 prize if exactly four of your six numbers appear on the winning ticket. In a given lottery drawing, how many different tickets would win the Match-4 prize?

    \left(\left({6\atop 4}\right)\right) = \left({6+4-1\atop 4}\right) = 126

    Thanks
    No, I don't think that is correct.

    There are \binom{6}{4} ways to pick the matching 4 numbers, and there are \binom{34}{2} ways to pick the non-matching numbers. So...
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  3. #3
    Member oldguynewstudent's Avatar
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    Quote Originally Posted by awkward View Post
    No, I don't think that is correct.

    There are \binom{6}{4} ways to pick the matching 4 numbers, and there are \binom{34}{2} ways to pick the non-matching numbers. So...
    You are correct. Thank you. I'm still trying to get the hang of this.
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