Let $$S\,$$ be a set with six elements. In how many different ways can one select two not necessarily distinct subsets of $$S\,$$ so that the union of the two subsets is $$S\,$$? The order of selection does not matter; for example, the pair of subsets $$\{a, c\}\,$$, $$\{b, c, d, e, f\}\,$$ represents the same selection as the pair $$\{b, c, d, e, f\}\,$$, $$\{a, c\}\,$$.

(第十一届AIME1993 第8题)