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Question: Everybody in a room shakes hand with everybody else. The total number of hand shakes is 66. The tota...

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

A

11

B

12

C

13

D

14

Answer

12

Explanation

Solution

nC2=66⇒n(n−1)=132⇒n=12nC_{2} = 66 \Rightarrow n(n - 1) = 132 \Rightarrow n = 12.