The Florida lottery uses a system of numbers ranging in value from 1 to 49. Every week the lottery commission randomly selects six numbers, and every ticket with those numbers wins a share of the grand prize. Individual numbers appear only once (no repeat values), and the order in which they are chosen does not matter.
(a) What is the probability that a person buying one ticket will win the grand prize?
(b) The lottery also pays a lesser prize for tickets with five of the six numbers matching. What is the probability that a person buying one ticket will win either the grand prize or the lesser prize?
(c) The lottery also pays smaller prizes for getting three or four numbers matching. What is the probability that a person buying one ticket will win anything? That is, what is the probability of getting six matching numbers, or five matching numbers, or four matching numbers, or three matching numbers?