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no of unequal subsets of X={1,2,3,...,10} so that A\cap B={2,3,5,7}

Source: CRMO 2012 Region 1 p4

September 30, 2018

SubsetscombinatoricsCombinatorics of set

Problem Statement

Let

X=\{1,2,3,...,10\}

. Find the number of pairs of

\{A,B\}

such that

A\subseteq X, B\subseteq X, A\ne B

and

A\cap B=\{2,3,5,7\}