Thread: Lottery Probability

1. 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.

2. 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 $2 per play. (a) Find the number of possible outcomes. Five numbers are chosen from fifty-nine: .$\displaystyle _{59}C_5 \:=\:{59\choose5} \:=\:5,\!006,\!386$ways. One Powerball is chosen:$\displaystyle 35$ways. Therefore: .$\displaystyle 5,\!006,\!386 \times 35 \:=\:175,\!223,\!510$outcomes. (b) Find the number of ways to match 3 numbers and the Powerball. There are 5 "winners" and 54 "non-winners". To match exactly three numbers . . we must have 3 of the winners: .$\displaystyle _5C_3 \:=\:10$ways . . and 2 of the non-winners: .$\displaystyle _{54}C_2 \,=\,1431$ways. To match the Powerball, there is$\displaystyle 1$way. Therefore, there are: .$\displaystyle 10 \times 1431 \times 1 \:=\:14,\!310\$ ways.