For a particular lottery, the winning numbers are selected by a machine that randomly chooses 5 table-tennis balls from among 45, numbered 1 to 45. The lottery pays off if you match 5, 4, or 3 of the numbers.

a). How many different winning number combinations are there ?

b). What is the probability that you will match all 5 of the winning numbers ?

c). What is the probability that you will match exactly 4 of the 5 winning numbers ?

Thank you.