After a get-together every person present shakes the hand of every other person. If there were 105 hands shakes in all, how many persons were present in the party?

Options

A. 1. 14
B. 2. 13
C. 3. 15
D. 4. 16

Answer

C

Explanation

Let the total number of persons =n.
Then, according to the question, `""^nC_2 = 105`
or, `(n(n-1))/2 = 105 `
or, `n^2 - n = 210`
or `n^2 - n - 210 =0`
or, `(n - 15) (n - 14) = 0`
or `n = 15`
or, `n = -14` [`because` n cannot be negative]
`therefore n=-14 `is discarded.
So, `n = 15`.
Therefore, the total number of persons present at the get together = 15.