Lottery Probability

**renolovexoxo** · September 28th 2012, 12:58 PM

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.

**Soroban** · September 28th 2012, 02:08 PM

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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