Let S={1,2,3,…,n}. Three subsets A,B,C of S are chosen at random. Find the probability that A⊆B⊆C.
A⊆B⊆Cjust means all elements of A are elements of B and all elements of B are elements of 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.
B is not strictly one element less than C.
