Problem #WSP-5603

Problems Combinatorics

Problem

Elections are approaching in Problemland! There are three candidates for president: \(A\), \(B\), and \(C\).

An opinion poll reports that \(65\%\) of voters would be satisfied with \(A\), \(57\%\) with \(B\), and \(58\%\) with \(C\). It also says that \(28\%\) would accept \(A\) or \(B\), \(30\%\) \(A\) or \(C\), \(27\%\) \(B\) or \(C\), and that \(12\%\) would be content with all three candidates.

Show that there must have been a mistake in the poll.