Question

There are 22 people in a room, if everyone shakes everyone else’s hand exactly one time, how many handshakes would that be total?

Answer 1

There will be 231 handshakes in total

Solution:

There are 22 people in a room

Everyone shakes everyone else’s hand exactly one time

To find: Total number of handshakes in total

Let,

n = total number of people that will shake hands

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

(n - 1) = people would each shake hands

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

n(n - 1)

but that counts every handshake twice, so we have to divide by 2

Therefore;

`(n(n-1))/(2)`

Here, n = 22

`(n(n-1))/(2) = (22(22-1))/(2) = 11 * 21 = 231`

Thus there will be 231 handshakes in total