Powerball! The Powerball lottery picks five different integers between 1 and 59 inclusive, and a sixth integer between 1 and 39, which may duplicate one of the earlier five integers.
A participant of the lottery wins the jackpot if the first five numbers she picked match the first five numbers drawn (regardless of the order), and the sixth number she picked matches the sixth number drawn.
a. How many different tickets can a person buy? For the remaining subproblems, assume that the person just bought one ticket.
b. What is the probability her sixth number matches the sixth number drawn?
c. What is the probability that her first five numbers matches the first five numbers drawn, but her sixth number doesn't match the sixth number drawn?
d. What is the probability that the player matches exactly three of the first five numbers drawn and the sixth number drawn?
e. Finally, what is the probability that she wins the jackpot?