If two subsets \( A \) and \( B \) of set \( S \) containing \( n \...

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If two subsets \( A \) and \( B \) of set \( S \) containing \( n \) elements are selected at random, then the probability that \( A \cap B=\phi \) and \( A \cup B=S \) is
\( \mathrm{P} \)
(A) \( \frac{1}{2} \)
(B) \( \frac{1}{2^{n}} \)
(C) \( \left(\frac{3}{4}\right)^{4} \)
(D) \( \frac{1}{3^{n}} \)
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