Practice | Hashtable

1. 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.

A. 15

B. 14

C. 21

D. 25

Solution:

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,

\begin{aligned} ^{n} C_{2} = 105 \\ or, \frac{n!}{2! \times (n - 2)!} = 105 \\ or, \frac{n \times (n - 1)}{2} = 105 \\ or, n^{2} - n = 210 \\ or, n^{2} - n - 210 = 0 \\ or, n = 15, - 14 \end{aligned}

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

You must login to add comments. Login now.