12. The Powerball lottery is played twice each week in 23 states, the Virgin Islands, and the District of Columbia. To play Powerball a participant must purchase a ticket for $1 and then select five numbers from the digits 1 through 53 and a Powerball number from the digits 1 through 42. To determine the winning numbers for each game, lottery officials draw five white balls out of a drum with 53 white balls, and one red ball out of a drum with 42 red balls. To win the jackpot, a participant’s numbers must match the numbers on the five white balls in any order and the number on the red Powerball. In August 2001, four winners shared a jackpot of $295 million by matching the numbers 8-17-22-42-47 plus Powerball number 21. In addition to the jackpot, a variety of other prizes is awarded each time the game is played. For instance, a prize of $100,000 is paid if the participant’s five numbers match the numbers on the five white balls (http://www.powerball.com, March 25, 2003).

a. Compute the number of ways the first five numbers can be selected.

b. What is the probability of winning a prize of $100,000 by matching the numbers on the five white balls?

c. What is the probability of winning the Powerball jackpot?