This question is quite difficult , which can come in olympial or any other compitative exam.
At a party, everyone shook hands with everybody else. There were 66 handshakes. How many people were at the party??
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no of handshakes =nC2=n!/(n-2)!(2)!
so n=no of handshakes =12
here we used combinations because in permutations AB is different from BA but in combinations both are same.
Note -: Since if two persons hand shake it means both shake their hands with each other.
So here A shakes hand with B is same as B shakes hand with a.