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Simple sets

Source: Indian RMO 2004 Problem 4

February 28, 2006

Problem Statement

Prove that the number of triples (A,B,C)(A,B,C) where A,B,CA, B, C are subsets of {1,2,…,n}\{ 1,2, \ldots , n \} such that A∩B∩C=ϕA \cap B \cap C = \phi , A∩B≠ϕA \cap B \not= \phi, C∩B≠ϕC \cap B \not= \phi is 7n−2.6n+5n7^n - 2 . 6^n + 5^n.
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