In the Powerball game, five different numbers between 1 and 59 will be drawn in succession, and then one number (the Powerball number) between 1 and 35 will be drawn. The player marks five different numbers between 1 and 59 and one number between 1 and 35 on a game card.
a. What is the size of the sample space?
b. What is the probability of matching all five numbers in any order plus matching the Powerball number?
c. What is the probability of matching none of the five numbers but matching the Powerball number?