A is a set containing \( n \) elements. A subset \( S_{1} \) of \( A \) is chosen. The set \( A ...

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A is a set containing \( n \) elements. A subset \( S_{1} \) of \( A \) is chosen. The set \( A \) is reconstructed by replacing the elements of \( S_{1} \). Again, a subset \( S_{2} \) of \( A \) is chosen and again the set is reconstructed by replacing the elements of \( S_{2} \). The number of ways of choosing \( S_{1} \) or \( S_{2} \) where \( S_{1} \) and \( S_{2} \) have one element common is
(a) \( 3^{n-1} \)
(b) \( n \cdot 3^{n-1} \)
(c) \( 2^{n-1} \)
(d) \( n \)
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