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Every two persons shakes hands with eac...

Every two persons shakes hands with each other at a party and the total number of handshake is 66. The number of guests in the party is?

A

11

B

12

C

13

D

14

Text Solution

Verified by Experts

The correct Answer is:
B
Let the total number of person in the room is n.
We know that, two person form 11 hand shaken.
`therefore` Required number of hand shakes `= ""^(n)C_(2) = (n"!")/(2"!"(n-2)"!") = (n(n-1))/(2)`
According to the question, `(n(n-1))/(2) = 66`
`rArr` `n(n-1) = 132`
`rArr` `n^(2)- n - 132 = 0`
`rArr` (n-12)(n + 11) = 0
`rArr` `n= 12, - 11 " "` [inadmissible]
`therefore` n = 12
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