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) 13	B) 15	C) 12	D) 7	E) 9
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, n^2-n = 210;   Or, n^2-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.   Ans: 15
<result>B</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.