Question

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

Answer 1

The number of handshakes that will be there is;

`15\text{ }`

Step-by-step 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=(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=(6!)/(2!(6-2)!)=(6!)/(2!*4!) \\ ^6C_2=(1*2*3*4*5*6)/(1*2*1*2*3*4)=(30)/(2) \\ ^6C_2=15 \end{gathered}`

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

`15\text{ }`