The powerball lottery is played twice each week in 28 states, the virgin islands, and the district of colombia. to play powerball a participant must purchase a ticket and then select five numbers from the digits 1 through 55 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 55 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 number on the red power ball. in addition to the jackpot, a variety of other prizes are awarded each time the game is played. for instance, a prize of $200,000 is paid if the participant's five numbers match the numbers on the five white balls.

a. Compute the number of ways the first five numbers can be selected.
b. what is the probability of winning a prize of 200,000 by matching the numbers on the five white balls?
c. what is the probability of winning the Powerball jackpot?