Question

# Everybody in a room shakes hands with everybody else. If number of hand shakes is $$66$$. Then total number of persons in the room is

A
12
B
13
C
11
D
14

Solution

## The correct option is B $$12$$Let number of person in the room is $$n$$.Then if everybody shakes hands with everybody else then number of hand shakes is $$^nC_2$$.According to the problem,$$^nC_2=66$$or, $$n(n-1)=132$$or, $$n^2-n-132=0$$or, $$(n+11)(n-12)=0$$or, $$n=12$$. [ Since $$n\ne -11$$]So total number of person in the room is $$12$$.Mathematics

Suggest Corrections

0

Similar questions
View More

People also searched for
View More