Question

In the conference of $8$ persons, every person handshake with each other only one,then find the total number of hand shaked.

Answer 1

Let $n$ be the total number of persons in the conference. Since every person handshake with each other only once, then, the number of handshakes can be calculated by ${}^n{C}_2$, here 2 refers to the pair of hands of each person.

${}^8{C}_2=\frac{8!}{2!\left(8-2\right)!}$

$=\frac{8!}{2!6!}$

$=28$

Therefore, the total number of handshakes are 28.