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;

$\frac{n(n-1)}{2}$

Here, n = 22

$\frac{n(n-1)}{2} = \frac{22(22-1)}{2} = 11 \times 21 = 231$

Thus there will be 231 handshakes in total