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CEMC Gauss (Grade 8), 2006

Combinatorics Difficulty 2.0 Junior Find the answer Canada

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?

(A) $3$ (B) $4$ (C) $5$ (D) $6$ (E) $7$

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