ShmoopTube

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Here’s your shmoop du jour, brought to you by Handshakes.

00:06

The best way to pass along bacteria to someone you’ve just met.

00:09

Six people are in a room.

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If everyone shakes hands one time with each other, how many handshakes take place?

00:18

Okay, so either some important business deal is about to go down…

00:21

…or else the annual Sweaty Palm Convention is in town.

00:24

Purell, anyone?

00:26

All right – we’re looking for the total number of handshakes.

00:29

First, each of the 6 people has to shake hands with the 5 other people.

00:34

To count these handshakes, let’s multiply 6 by 5... 30.

00:39

Oops. By doing that, we’ve over counted… by a lot.

00:43

With this method, we’re basically counting person A shaking hands with person B as one handshake

00:49

and person B shaking hands with person A as a totally separate handshake.

00:54

In reality, when 2 people shake hands with each other, that only counts as 1 handshake.

01:00

To be more specific, our number is actually double the real number of handshakes actually happening,

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so divide that 30 by 2 and get 15.

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That’s a lot of handshaking.

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