AMC 10 2008a Problem 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? $\mathrm{(A)}\ 20 \mathrm{(B)}\ 40 \mathrm{(C)}\ 60 \mathrm{(D)}\ 160 \mathrm{(E)}\ 320$