After a student council meeting, all 14 members shook hands with every member. how many handshakes were made?

There are 2 ways to solve this.


Method 1:

The 1st person will shake hand with the other 13 members.
The 2nd person will shake hand with the other 12 members.
The 3rd person will shake hand with the other 11 members
This goes on until all the hands are shake.

So number of handshake:
13 + 12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 91


91 handshakes are made.



Method 2:

There are 14 people. Each handshake consisted of 2 person. Consider how many different ways we can choose to pair the 2 person.
Mathematically, it would be 14 x 13 = 182

But Person A shaking hand with Person B is the same as Person B shaking hand with Person A. So we have double count it. We divide the number by 2.

182 ÷ 2 = 91


91 handshakes are made.