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Question

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

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Solution

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

Explanation:

Say we have N people in the room. So to shake hands we have to pair each one of these N with each one of the rest of people in the room.

So we have N(N1) possible pairings.

However, in this number we have actually counted each pairing twice; when, say person1 shakes hands with person2, and when person2 shakes hands with person1. It is only one handshake.

Thus, the correct number is half of that N(N1)2

=20(201)2=10×19=190


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