Question

There are 15 persons in a party and if each 2 of them shakes hands with each other, how many handshakes happen in the party?

Answer 1

Total number of person in the party = 15

Given if each 2 of the 15 persons shakes bands with each other.

∴ The total number of handshakes is same as the number of ways of selecting 2 persons among 15 persons.

This can be done in 15C₂ ways.

Number of handshakes = 15C₂ 

= `(15!)/(2!(15 - 2)!)`

= `(15!)/(2! xx 3!)`

= `(15 xx 14 xx 13!)/(2 xx 1 xx 13!)`

= 15 × 7

= 105