In the Powerball® lottery, the player chooses five numbers from the first field of 59 numbers and one "Powerball" number from the second field of 35 numbers. A player wins the jackpot if all six of the player's numbers match the six winning numbers.

(a) How many different possible ways are there select the six numbers?

(b) How many tickets would someone have to purchase to have at least a one in a million chance of winning the jackpot?

(c) What is the probability that none of the player's numbers match any of the six winning numbers? (Assume this player only has one ticket.)

(d) The player wins the second prize if the player matches the first five numbers but does not match the Powerball. The player wins third prize if the player matches the Powerball but only matches four of the other five numbers. What is the probability that a player who buys a single ticket will win at least third prize?