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Math Help - Lotto Game

  1. #1
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    Lotto Game

    Rules of the Game:

    1. Player selects 5 numbers 1-47.
    2. Player selects a "special" number 1-27.
    3. Five numbers are drawn and a special number is drawn.

    What is the probability that the player matches three of five numbers and the special number?


    Attempt:

    I want to divide the "favorable" outcomes by the total number of possibilities. The total number of possibilities seems to be 47^5 X 27.

    Now, the hard part seems to be the favorable outcomes. That is, how many combinations yield exactly 3 matches and 1 match with the special number?

    Any help would be appreciated.
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  2. #2
    MHF Contributor Unknown008's Avatar
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    No, this involves combinations.

    The possible number of outcomes with 5 numbers from 47 numbers is 47C5
    Now, there is one more, number to pick out of 27, hence 27 possible ways

    For a total of 27*47C5 possible combinations. (ie 41416353)

    Now, for the favourable outcomes part:

    Ways to get 3 matching numbers = 5C3 (3 good numbers from the 5 numbers which were drawn)

    Then, the rest, being = 42C2 (ie, 2 of the 42 numbers not drawn)

    And of course, there is only 1 out of 1 way to pick the good number.

    For a total of 5C3 x 42C2 x 1
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  3. #3
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    thanks my man!
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