Let \(S = \{1,2,3, \dots, n\}.\) Three subsets \(A,B,C\) of \(S\) are chosen at random. What is the probability that \(A \subseteq B \subseteq C\)?
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.