SOLUTION
Step 1 :
a ) In the first part of the question, we are meant to find how many ways
in which six roles can be assigned if there are 6 people for an audition,
we have that :
[tex]6\text{ }!\text{ = 6 x 5 x 4 x 3 x 2 x 1 = 720 ways}[/tex]
b ) For the second part of the question, we are meant to find how many ways
in which six roles can be assigned if there are 9 people for an audition.
we have that:
[tex]\begin{gathered} 9\text{ }P\text{ 6 =}\frac{\text{ 9}!}{(\text{ 9 - 6 )}!} \\ =\frac{9!}{3!} \\ =\text{ 9 x 8 x 7 x 6 x 5 x 4 } \\ =\text{ }60,\text{ 480 ways.} \end{gathered}[/tex]
