Question

Everybody in a room shakes hands with eacg other the total no of hand shakes is 66 how many people are there in the room

Answer 1

Answer:

12

Step-by-step explanation:

Here each person will shake hand with another which means 2 person will shake hand at a time.

So,

nC2 = 66

n!/(n-2)!2! = 66

n(n-1)(n-2)!/(n-2)!2! = 66

n(n-1)/2 = 66

n^2-n = 66*2

n^2-n = 132

n^2-n-132 = 0

n^2-12n+11n-132 = 0

n(n-12)+11(n-12) = 0

(n-12)(n+11) = 0

So, n= 12 or -11

But number of persons can't be negative so we'll consider the positive value of n which is 12

Thus, 12 people are there in the room.