Easy formula for solving Handshake maths problem

                       

            Handshake Problem

At a conference 12 members shook hands with each other before & after the meeting.

How many total no of handshakes occured?
_________

Before we're going to imagine situation of handshake problem , I hope we can  get the formula before starts daydreaming.

In meetings  ,handshakes is just greetings & parting tradition.

Well imagine !

If there is a maths professor among them.
Who humorously asked the above question in front of everyone.

'Everyone's eye will be one you'

What will you do?

Can you solve it?

Don't worry 

See the solution below



Let's take there are 5 members
A,B,C,D & E.

A shakes hands with B,C,D,E.
B shakes hands with C,D,E. [A-B already shaken hands]

C shakes hands with D,E [ C has already shaken hands with A& B]

D shakes hands with E [ D has already shaken hands with A,B & C]

For E, he has  already shaken hands with everyone.

So total no .  of  handshakes.

4+ 3 + 2 + 1+ 0 =  10

Similarly,

No.  of handshakes between 12 members

11+ 10+ 9+ 8+ 7+6 + 5 + 4 + 3 + 2 + 1=66

But according to question they shaken hands both before & after meeting

So 2×66= 132

ANS: 132

But what if 

there are n members.???

Just use combination formula given below:

Formula:

 nC2 = n(n-1)/2


Easy simple formula to solve handshake problem 👆