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.
You are creating passwords of length \(8\) using only the letters \(A\), \(B\), and \(C\). Each password must use all three letters at least once.
How many such passwords are there?
How many numbers from \(1\) to \(1000\) are divisible by \(2\) or \(3\)?