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.
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.
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.