At a regional mathematics conference, there are 12 students. Every student shakes hands with every other student exactly once, except for two students who refuse to shake hands with each other at all. What is the total number of handshakes that take place?

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• A 66
• B 65
• C 55
• D 54

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Answer: B. 65

If everyone shook hands, there would be 12C2 = (12 × 11)/2 = 66 handshakes.
One pair does not shake hands, so the total is 66 - 1 = 65.

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