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Question

Everybody in a room shakes hands with everybody else. If number of hand shakes is $$66$$. Then total number of persons in the room is


A
12
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B
13
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C
11
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D
14
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Solution

The correct option is B $$12$$
Let number of person in the room is $$n$$.
Then if everybody shakes hands with everybody else then number of hand shakes is $$^nC_2$$.
According to the problem,
$$^nC_2=66$$
or, $$n(n-1)=132$$
or, $$n^2-n-132=0$$
or, $$(n+11)(n-12)=0$$
or, $$n=12$$. [ Since $$n\ne -11$$]
So total number of person in the room is $$12$$.

Mathematics

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