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

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Consider all \( 2^{n}-1 \) non-empty subsets of the set \( \{1,2 \), \( 3, \ldots \ldots n\} \). For every such subset we find the product
\( \mathrm{P} \)
of each of its elements. Sum of all these product is
W.
(1) \( (n+1) \) !
(2) \( (n+1) !+1 \)
(3) \( (n+1) !-1 \)
(4) \( n !-2 \)


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