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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!

 Jun 12, 2020
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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.

 Jun 12, 2020

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