Let \(S=\{1, 2, 3,\dots, n\}.\) Three subsets \(A, B, C\) of \(S\) are chosen at random. Find the probability that \(A\subseteq B\subseteq C.\)
\(A\subseteq B\subseteq C\)just means all elements of \(A\) are elements of \(B\) and all elements of \(B\) are elements of \(C.\)
