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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?

 May 24, 2020
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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)

 

OR

How many ways can I take pairs form the circle         40C2 = 780

 

I cannot be wrong twice .... OR can I ???

 May 24, 2020

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