HMMT November 2013 U13

Let $S=\{1,2, \ldots, 2013\}$ . Find the number of ordered triples $(A, B, C)$ of subsets of $S$ such that $A \subseteq B$ and $A \cup B \cup C=S$ .

Dataset text NuminaMath olympiads. Quoted with source.

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5^{2013}

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