Consider all \( 2^{n}-1 \) non-empty subsets of the set \( \{1,2,3,...

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Consider all \( 2^{n}-1 \) non-empty subsets of the set \( \{1,2,3, \cdots n\} \). For every such subset we find the product of each of its elements. Sum of all these products is
(a) \( (n+1) \) !
(b) \( (n+1) !+1 \)
(c) \( (n+1) !-1 \)
(d) \( n \) ! \( -2 \)
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