Question 155

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?

Solution

The total number of handshakes between two people, such that each person shakes with another person, is $$^nC_2$$.

Let us assume the total number of persons present at the party is = n

Thus, we know the value of $$^nC_2$$ = 105

$$^nC_2=\frac{n!}{\left(n-2\right)!2!}$$

=> $$\frac{n\left(n-1\right)}{2}=105$$

n(n-1) = 210

Thus, the value of n = 15

As, 15*14 = 210

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