Question

एक कमरे में प्रत्येक ने प्रत्येक से हाथ मिलाया । कुल 66 बार हाथ मिलाया गया । कमरे में कुल व्यक्ति है ।​

Answer 1

x c 2 = 66

where x is the no of people

c is combination

and 2 is the hand shake as 2 people do at a time

using formulae

x! /x-2!×2!=66

x²-x-132=0

x²-12x+11x-132=0

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

(x-12)or (x+11)=0

x=12

there were 12 people in the room

Answer 2

There are 12 people in a room.

Step-by-step explanation:

Let n be the no. of people

No. of handshakes between 2 people = 1

We will use combination

Formula :$^nC_r=\frac{n!}{r!(n-r)!}$

So, No. of possible handshakes =$^nC_2$

We are given that total no. of handshakes are 66

So, $^nC_2=66$

$\frac{n!}{2!(n-2)!}=66$

$\frac{n(n-1)(n-2)!}{2!(n-2)!}=66$

$\frac{n(n-1)}{2 \times 1}=66$

$n^2-n=132$

$n^2-n-132=0$

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

n=12,-11

Since no. of people cannot be negative

So, There are 12 people in a room.

#Learn more:

If each student meets their classmate with a handshake and there are 20 students how many handshakes will happen

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