Question 324197
For the first person, there will be 11 handshakes.
For the second person, there will be 10 handshakes because that person has
shaken the hand of the first person.
So for the third there will be 9 handshakes and so on and so on.

So there will be 11+10+9+8+7+6+5+4+3+2+1   handshakes.

This is equal to (12*11)/2= 66

If there are n people in the room, then there are n(n-1)/2 handshakes.