Question

read the problem below and solve the solution draw a diagram on your paper to help solve it

Answer 1

Answer:

The number of handshakes that will be there is;

$15\text{ }$

Explanation:

Given that there are 6 people in the party.

And each person must shake hands with every other person exactly once.

So, since order is not improtant, we have;

$^nC_r=\frac{n!}{r!(n-r)!}$

For this question;

$\begin{gathered} n=6 \\ r=2\text{ ( the number of persons involved in a single hand shake)} \end{gathered}$

It then becomes;

$\begin{gathered} ^6C_2=\frac{6!}{2!(6-2)!}=\frac{6!}{2!\times4!} \\ ^6C_2=\frac{1\times2\times3\times4\times5\times6}{1\times2\times1\times2\times3\times4}=\frac{30}{2} \\ ^6C_2=15 \end{gathered}$

Therefore, the number of handshakes that will be there is;

$15\text{ }$