Question

Everybody in a room shakes hand with everybody else. The total number of hand shakes is 66. Then find the total number of persons in the room.


Answer is 12. I want to know the method.
Pls answer only if you know the method.

Answer 1

Hey. Your answer is 12.
The method is attached in the image.
Hope it helps you.

Mark as brainliest if it helps you

Answer 2

Answer : The total number of persons in room are 12 Step-by-step Explanation : Given : Everybody in a room shakes hand with everybody else. The total number of hand shakes is 66. To find : The total number of persons in the room = ? Let the total number of persons in the room be 'n' (Here we will apply the concept of combination) Therefore Required number of Hand Shakes = nC2 = n( n - 1 ) / 2 According to given conditions, n( n - 1 ) / 2 = 66 n( n - 1 ) = 66 × 2 n( n - 1 ) = 132 n² - n - 132 = 0 Simplifying the above Quadratic Equation we get ( n - 12 ) ( n + 11 ) = 0 n = 12 or n = -11 But since n can't be negative so n = 12 Hence the total number of persons in room are 12