In a certain state's lottery, 40 balls numbered 1 through 40 are placed in a machine and 7 of them are drawn at random. If the 7 numbers drawn match the 7 numbers a player has chosen, in any order, she or he win $2,500,000. Alternatively, if 6 of the numbers drawn match 6 of the 7 numbers a player has chosen, in any order, the player wins $40,000, and if 5 of the numbers drawn match 5 of the 7 numbers a player has chosen, in any order, the player wins $10,000. Required:
a. What is the probability a player who buys one ticket will win the $2,500,000 prize?
b. What is the probability a player who buys one ticket will win the $10,000 prize?