Question

At a get together 22 people shake their hands with each other . How many handshakes took place in all?

Answer 1

Let's consider the names of 22 people as A,B,C,D......V.

So firstly A decides to make handshakes with 21 other people.

Hence 21 handshakes.

Secondly B decides to make handshakes. But he has already shaken hands with A. Thus he is left with only 20 people to make handshakes.

Thus 20 handshakes.

Similarly C - 19
D - 18
E - 17
..........U-1 V-0

So total number of handshakes = 1+2+3+.......+20+21.

which is the sum of natural numbers from 1 to 21 = 21*(21+1)÷2
=21*22÷2
=21*11
=231



Generallythe formula to count handshakes is

n*(n−1)/2

Where n is the number of people