A player in the Mega Millions lottery picks five different integers between 1 and 56. inclusive, and a sixth integer between 1 and 46, which may duplicate one of the earlier five integers.

The player wins the jackpot if the first five numbers picked match the first five numbers drawn and the sixth number matches the sixth number drawn.

a) What is the probability that a player wins the jackpot?

b) What is the probability that a player wins $250,000. which is the prize for matching the first five numbers, but not the sixth number, drawn?

c) What is the probability that a player wins $150 by matching exactly three of the first five numbers and the sixth number or by matching four of the first five numbers but not the sixth number?

d) What is the probability that a player wins a prize, if a prize is given when the player matches at least three of the first five numbers or the last number.