Answered

If you have six people in a room, and each person shakes hands with every other person

exactly once, how many total handshakes happen?

A6 (B) 12 (C) 15 (D) 21 (E) 720

Verified Answer :

CrimmyTheCreator

D Is the correct answer. I'm pretty sure.

Apocrophon

The way you can show this is;
(people labeled 1-6)
6 + 5 | 5 + 4 | 4 + 3 | 3 + 2 | 2 + 1
6 + 4 | 5 + 3 | 4 + 2 | 3 + 1
6 + 3 | 5 + 2 | 4 + 1
6 + 2 | 5 + 1
6 + 1 | 

There are 30 possible combinations, but if they shake hands with every other person, the number is halved.
\(\frac{30}{2} =15\)
This means that there are 15 handshakes total.

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