Let \(S = {1, 2, 3, \dots, n}\) Three subsets A, B, C of S are chosen at random.
Find the probability that \(A \subseteq B \subseteq C\)
I'm completely stuck on this, any help would be appreciated!
There are 2^n ways of choosing C, then 2^(n - 1) ways of choosing B, then 2^(n - 2) ways of choosing A, so the probability is 2^n*2^(n - 1)*2^(n - 2)/(2^n*2^n*2^n) = 1/8.
