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HMMT November 2010 U6

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How many ordered pairs (S,T)(S, T) of subsets of {1,2,3,4,5,6,7,8,9,10}\{1,2,3,4,5,6,7,8,9,10\} are there whose union contains exactly three elements?

Dataset text NuminaMath olympiads. Quoted with source.

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