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Sample Question 23:
Two subsets of the set \(S=\lbrace a,b,c,d,e\rbrace\) are to be chosen so that their union is \(S\) and their intersection contains exactly two elements. In how many ways can this be done, assuming that the order in which the subsets are chosen does not matter?
\(\mathrm{(A)}\ 20\qquad\mathrm{(B)}\ 40\qquad\mathrm{(C)}\ 60\qquad\mathrm{(D)}\ 160\qquad\mathrm{(E)}\ 320\)