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### Counting Handshakes

```
Date: 9/7/95 at 9:23:24
From: Anonymous
Subject: Math

Hello!

20 people in a room, each person shakes hands just once with everyone else.
Wouldn't this be 380 total handshakes? 19 * 20 = 380.

Thanks.
```

```
Date: 9/8/95 at 10:53:14
From: Doctor Ethan
Subject: Re: Math

Howdy,

Well, you are fairly close,  but your reasoning is a little bit off.

For the first person, there will be 19 handshakes.
For the second there will be 18 handshakes because that person has already
shaken the hand of the first person.
So for the third there will be 17 handshakes.

So there will be 19 +18+17 +16 +.....   handshakes.

This is equal to 19 * 20/2
See if you can figure out why.

Hope that helps,

- Doctor Ethan,  The Geometry Forum

```
Associated Topics:
High School Permutations and Combinations

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