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

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

Grade:12

1 Answers

Latika Leekha
askIITians Faculty 165 Points
6 years ago
Everybody shakes hands with everybody.
This means that n people shake hands with (n-1) people.
Hence, the total number of handshakes are n(n-1).
Now, each handshake involves 2 people, and each event of handshake involves repetition of half handshakes.
Hence, the total number of handshakes are ½ n(n-1).
Thus, we have ½ n(n-1) = 66.
This gives n2 – n -132 = 0
(n-12)(n+11) = 0.
This gives n = 12. (Since the number of people cannot be negative)
Hence, there are 12 people in the room.
Thanks & Regards
Latika Leekha
askIITians Faculty.

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