4.120 Winning the Lottery On Wednesday, October 26, 2005, a single winning Lotto 6/49 lottery ticket was sold in Camrose, Alberta. The ticket belonged to 17 oil industry workers. According to the Alberta Lottery Fund, the winning numbers were 5, 11, 20, 30, 37, and 43. The prize was $54,000,000.

a. How many ways can six numbers be picked from 49, without replacement?

b. If exactly one ticket is purchased, what is the prob- ability of being a winner?

c. How many different orders of the numbers 5, 11, 20, 30, 37, and 43 are possible?