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. Choose the correct option:
A) 14 B) 12 C) 13 D) 15 E) 16
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.   Option 15
<result>D</result>
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.