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Math Help - Counting Methods ???

  1. #1
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    Counting Methods ???

    In a lotto, a player picks a selection of 6 numbers from the numbers 1 to 45. To determine the winners 8 numbers are chosen at random - the first 6 are designated as the winning numbers, and the other 2 as supplementary numbers.
    Division 1: 6 winning numbers
    Division 2: 5 winning numbers and 1 supplementary
    Division 3: 5 winning '
    Div 4: 4 winning '
    Div 5: 3 winning ' and 1 supplementary
    Find the number of combinations which satisfy each of the divisions, and hence the probabilities of winning each of the five divisions.

    I don't get a word of it....
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  2. #2
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    Quote Originally Posted by cookie View Post
    In a lotto, a player picks a selection of 6 numbers from the numbers 1 to 45. To determine the winners 8 numbers are chosen at random - the first 6 are designated as the winning numbers, and the other 2 as supplementary numbers.
    Division 1: 6 winning numbers
    Division 2: 5 winning numbers and 1 supplementary
    Division 3: 5 winning '
    Div 4: 4 winning '
    Div 5: 3 winning ' and 1 supplementary
    Find the number of combinations which satisfy each of the divisions, and hence the probabilities of winning each of the five divisions.

    I don't get a word of it....
    Well 6 winning numbers, how many combinations exist?

    {45 \choose 6} = 8,145,060

    thus the probability p(6 winning numbers) = 1 / 8,145,060

    and so on...
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