+563 Let n be a positive integer, and let S = {1, 2, 3, ..., n}. Three subsets A, B, C of S are chosen at random.
(a) Find the probability that A contains all elements 1, 2, 3, ..., n.
(b) Find the probability that B contains all the even numbers.
(c) Find the probability that C contains all the odd numbers.
