2006 Gauss 8 Problem 22

The 8 people at a party shook hands exactly once with each of the others before the ninth person arrived. The ninth person then shook hands with some of these 8 people. A total of 32 handshakes took place. With how many people did the ninth person shake hands?

\textbf{(A)}\ 3\quad \textbf{(B)}\ 4\quad \textbf{(C)}\ 5\quad \textbf{(D)}\ 6\quad \textbf{(E)}\ 7

If there are no answer choices shown, enter a numerical answer.

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