It\'s Fall again and time for Vermont homeowners to deal with mice coming indoor

Question

It's Fall again and time for Vermont homeowners to deal with mice coming indoors to seek refuge from the cold. 14 local Vermonters met one night at the Grange to share their ideas about how to deal with the rodents. The 14 Vermonters were all happy to see each other again (they hadn't all been together since last Winter when they decided to get some indoor plumbing in the Hal), and they all exchanged hellos. How many handshakes were exchanged so that everyone shook hands with everyone else at the meeting?

Explanation / Answer

answer is 91

there are 14 vermonters and one handshakes were exchanged between two persons

so number of handshake exchanged among 14 vermonters =14C2=14!/(12!*2!)=14*13/2=91

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