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Turkish NMO First Round - 2012 Problem - 08 {Combinatorics}

Source:

July 1, 2012
algebrabinomial theorem

Problem Statement

In how many different ways can one select two distinct subsets of the set {1,2,3,4,5,6,7}\{1,2,3,4,5,6,7\}, so that one includes the other?
<spanclass=latexbold>(A)</span> 2059<spanclass=latexbold>(B)</span> 2124<spanclass=latexbold>(C)</span> 2187<spanclass=latexbold>(D)</span> 2315<spanclass=latexbold>(E)</span> 2316 <span class='latex-bold'>(A)</span>\ 2059 \qquad <span class='latex-bold'>(B)</span>\ 2124 \qquad <span class='latex-bold'>(C)</span>\ 2187 \qquad <span class='latex-bold'>(D)</span>\ 2315 \qquad <span class='latex-bold'>(E)</span>\ 2316