If there are 12 persons in a party and each of them shakes hands with each other, how many handshakes do happen in the party?

first person will shake hands with 11 other persons. Seconds person will shake hands with 10 other persons, Third person will shake hands with 9 other person and so on.
So , total handshake
= 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 = 66
OR
2 person are to be chosen from 12 person to have a hand shake
∴ Possible ways = ¹²C₂ = 12! / 2!(12 - 2)! = 66