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Math Help - Lottery Probability

  1. #1
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    Lottery Probability

    I'm having trouble answering part b in this problem. I am very bad with combinations and since there are many parts to follow, I was hoping someone might be able to explain it to me. When I did it I got like 10 options, which I know isn't correct.
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  2. #2
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    Re: Lottery Probability

    Hello, renolovexoxo!

    PowerBall: Five numbers are drawn from the set 1 - 59.
    The Powerball is drawn from the set 1 - 35. The cost is $2 per play.

    (a) Find the number of possible outcomes.

    Five numbers are chosen from fifty-nine: . _{59}C_5 \:=\:{59\choose5} \:=\:5,\!006,\!386 ways.
    One Powerball is chosen: 35 ways.

    Therefore: . 5,\!006,\!386 \times 35 \:=\:175,\!223,\!510 outcomes.




    (b) Find the number of ways to match 3 numbers and the Powerball.

    There are 5 "winners" and 54 "non-winners".

    To match exactly three numbers
    . . we must have 3 of the winners: . _5C_3 \:=\:10 ways
    . . and 2 of the non-winners: . _{54}C_2 \,=\,1431 ways.

    To match the Powerball, there is 1 way.

    Therefore, there are: . 10 \times 1431 \times 1 \:=\:14,\!310 ways.
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