# 20 people shake hands with each other. How many handshakes will be there in total?

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We use this formula for this but why?

N(N-1)/2

20(20-1)/2

20 * 19/2

10 * 19

190

Can anybody explain this formula?

We use this formula for this but why?

N(N-1)/2

20(20-1)/2

20 * 19/2

10 * 19

190

Can anybody explain this formula?

##### 2 Answers

Shaking hands in a group involves pairings of two people in all possible ways

#### Explanation:

Say we have

However, in this number we have actually counted each pairing twice; when, say **one** handshake.

Thus, the correct number is **half** of that

see a solution process below;

#### Explanation:

First using your method which is the formula for handshakes;

Note that;

but since all (total) can't shake hands with themselves, hence we subtract one individual to start the handshaking..

hence we multiply both total numbe persons with people that will shake hands;

but that counts every handshake twice, so we have to divide by

Therefore;

Secondly;

You know that the total number of persons is

It then mean that, there are

But by every handshake **two persons** are involved.

Hence;

Therefore,

Thirdly;

I just used normal simple combination formula..

Recall;

Inputing in the formula we should have;