Question

In a party, it was found that a total of 210 hand-shakes took place. If each guest shook hand only once with all the others, how many people were present?

Answer 1

This question can be solved using Combination method. The answer is 21 persons.

Every handshake invloves 2 people and every person handshakes with every other person once.

Let the number of persons be x.

Then by combination method,

xC2=210

[nCr=n!/{r!*(n-r)!}]

=>x*(x-1)/(2*1)=210 [Here only two terms are considered in numerator because r=2 and therefore all the other terms cancel each other.This is a shortcut]

=>x^2-x=420

=>x^2-x-420=0

Solving this equation we get 21 and -20 as answers.

Negative answer is neglected and therefore the answer is 21 persons.