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  • Everybody in a room shakes hands with everybody else. The total number of handshakes is 66. The total number of persons in the room is A. 11 B. 12 C. 13 D. 14

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

A. 11

B. 12

C. 13

D. 14

Answers (1)

The answer is the option b.

\\ \text { Number of hand shakes }=n_{C_{2}}=\frac{n !}{(n-2) ! 2 !}=\frac{n(n-1)}{2}=66 \\ n(n-1)=132 \\ n^{2}-n=132=0 \\ (n-12)(n+11)=0 \\ n=12

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