Question

15 men in a room shake hands with each other, then the total number of handshakes is

(a) 90 

(b) 105 

(c) 110 

(d) 115

Answer 1

(b) 105

Since every person in the room shakes hand with every other person.

So, total number of handshakes = Number of ways of selecting 2 men out of 15 men 

= ¹⁵C₂ = \(\frac{15!}{13!\times2!}=\frac{15\times14}{2}\) = 105.