In a party every person shakes hands with every other person. If there are 105 hands shakes, find the number of person in the party.

Explanation:-

Let n be the number of persons in the party. Number of hands shake = 105; Total number of hands shake is given by ⁿC₂.

Now, according to the question,

ⁿC₂ = 105;
Or, n!/[2!*(n-2)!] = 105;
Or, n*(n-1)/2 = 105;
Or, n²-n = 210;
Or, n²-n-210 = 0;
Or, n = 15, -14;

But, we cannot take negative value of n.
So, n = 15 i.e. number of persons in the party = 15.