Question

auditions are being held for the play shown. How many ways can the six roles be assigned ifA:6 people auditionB: 9 people audition

Answer 1

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 :

`6\text{ }!\text{ = 6 x 5 x 4 x 3 x 2 x 1 = 720 ways}`

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:

`\begin{gathered} 9\text{ }P\text{ 6 =}\frac{\text{ 9}!}{(\text{ 9 - 6 )}!} \\ =(9!)/(3!) \\ =\text{ 9 x 8 x 7 x 6 x 5 x 4 } \\ =\text{ }60,\text{ 480 ways.} \end{gathered}`