Question

In a party every person shakes hands with every other person. If there was a total of 105 handshakes in the party, find the number of persons who were present in the party.

Answer 1

Let no. of Persons be 'n' then

no. of handshakes ${=}^n{C}_2$

${\Rightarrow }^n{C}_2=105$

$\Rightarrow \frac{n!}{(n-2)!}=210\Rightarrow n^2-n-210=0$

$\Rightarrow n=15(\because n>0)$