Question

 

Everybody in a room shakes hands with everybody else. If total number of hand shakes is 66, then total number of persons in room is 

a) 11       b) 12 c) 13          d) 14​

Answer 1

$\huge\star{\tt{\underline{\underline{\red{Answer}}}}}\star$

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A person will shake a hand to other in one way

so here we are given that

$\implies$66 handshakes were occured

i.e

n be the no. of people

$^{n}C_{2}$=66

$\implies$ $\large\frac{n!}{(n-2) 2!}$=66

$\implies$ $\large\frac{n(n-1)}{2}$=66

$\implies$ n²-n=132

$\implies$ n²-n-132=0

Here when you solve the quadratic equation

you get the solution

n=-12,11

so we know that no.of people can't be negative

therefore,

$\huge{\boxed{\boxed{\tt{a)11}}}}$

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