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We are using PIE: to count the functions which are not surjective, we added up the functions which exclude \(a\text{,}\) \(b\text{,}\) and \(c\) separately, then subtracted the functions which exclude pairs of elements. We would then add back in the functions which exclude groups of three elements, except that there are no such functions. We find that the number of functions which are not surjective is

\begin{equation*} 2^5 + 2^5 + 2^5 - 1 - 1 - 1 + 0\text{.} \end{equation*}
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