Let \(S = \{1, 2, 3, \dots, n\}.\) Three subsets \(A, B, C\) of S are chosen at random.
(a) Find the probability that \(A \cup B \cup C = S.\)
(b) Find the probability that \(A \subseteq B \subseteq C \).
Explain all answers thoroughly.
Please help! Thanks!
