The powerball lottery is played twice each week in 31 states, the district of columbia and the virgin islands. To play powerball, a participant must purchase a $2 ticket, selest five numbers from the digits 1 through 59, and then select a powerball number from the digits 1 through 35. To determine the winning numbers for each game, lottery officials draw 5 white balls out of a drum of 59 white balls numbered 1 through 59 and 1 red ball out of a drum of 35 red balls numbered 1 through 35. To win the powerball jackpot, a participant's numbers must match the numbers on the 5 white balls in any order and must also match the number on the red powerball.
The numbers 5-16-22-23-29 with a powerball number 6 provided the record jackpot of $580 million.a) How many powerball lottery outcomes are possible?
(hint Consider this a two-step exsperiment. Select the 5 white ball numbers and then selectthe 1 red Powerball number)b) What is the probability that a $2 lottery ticket wins the powerball lottery?

Since the first five balls are selected without replacement, there are 59 possibilities for the 1st ball, 58 for the 2nd , 57 for the 3rd , 56 for the 4th and 55 for the 5th .

Then, there are 35 possibilities for the power ball.

a) How many powerball lottery outcomes are possible?

By the Fundamental Rule of Counting, there are

59*58*57*56*55*35 = 21,026,821,200

different outcomes.

b) What is the probability that a $2 lottery ticket wins the powerball lottery?

Since any number has the same probability of being drawn, the probability of winning is

[tex]\large\bf \frac{1}{21,026,821,200}[/tex]