There are 40 people in a room. All the people shake each other's hand once. (So if person 1 shook person 2's hand, person 2 shaking person 1's hand would not be a handshake.) How many handshakes occurred in all?
This question comes up regularly.
How about if all the people stand on the circumference of a circle.
Then you need to know how many lines must be drawn to join all the PAIRs of people
The first person will have 39 people to shake hands with and then that person can be removed from the circle
The second person will have 38 people to shake hands with and then that person can be removed from the circle.
The third person has 37 people etc
So that is 39+38+37+ ........+1 = 39/2(2+38*1)= 780 (that is an AP)
How many ways can I take pairs form the circle 40C2 = 780
I cannot be wrong twice .... OR can I ???