A player in the Mega Millions lottery picks five different integers between 1 and 70, inclusive, and a sixth integer between 1 and 25, inclusive, which may duplicate one of the earlier five integers. The player wins the jackpot (currently $126 million) if the first five numbers picked match the first five numbers drawn (in any order) and the sixth number picked matches the sixth number drawn. Required:
a. What is the probability that a player wins the jackpot?
b. What is the probability that a player wins the second prize ($1,000,000) by matching the first five numbers drawn (in any order) but not the sixth number?
c. What is the probability that a player wins $10 by matching exactly three of the first five numbers drawn (in any order) but not the sixth number or two of the first five numbers drawn (in any order) and the sixth number?