Over the summer, a group of math teachers from different schools got together for a BBQ. None of the teachers knew each other and each greeted the others with a handshake.
How many handshakes will occur at the party if every one of the 15 math teachers shakes hands with each of the others?
Show your work.
Answer (2)
The first partner in the handshake can be any one of 15 people. The second partner can be any one of 14 people. So the total number of possible arrangements is (15 x 14) = 210 .
BUT . . . .
If Mr. Smith and Mr. Jones are shaking hands, it doesn't matter which one is the first partner and which one is the second partner ... It's the same handshake either way.
That number of ' 210 ' up above counted both ways separately. The real number of handshakes between different people is half of that 210/2 = 105 handshakes .
There will be a total of 105 handshakes at the party with 15 math teachers. This is calculated using combinations to ensure each handshake is unique. Each teacher shakes hands with every other teacher exactly once.
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