Powerball is a game of chance that has generated intense interest because of its large jackpots. To play this game, a player selects five different numbers from 1 through 69, and then picks a Powerball number from 1 through 26. The lottery organization randomly draws 5 different white balls from 69 balls numbered 1 through 69, and then randomly picks a red Powerball number from 1 through 26. Note that it is possible for the Powerball number to be the same as one of the first five numbers.
a. If a player’s first five numbers match the numbers on the five white balls drawn by the lottery organization and the player’s red Powerball number matches the Powerball number drawn by the lottery organization, the player wins the jackpot. Find the probability that a player who buys one ticket will win the jackpot. (Note that the order in which the five white balls are drawn is unimportant.)

b. If a player’s first five numbers match the numbers on the five white balls drawn by the lottery organization, the player wins about $1,000,000. Find the probability that a player who buys one ticket will win this prize.