Question

there are 12 actors auditioning for 5 different roles in a new play. how many different cast are possible

Answer 1

Answer:

95,040 different cast are possible

Step-by-step explanation:

In this case the order in which the actors are selected for the 5 different roles is important. Therefore we use the permutations formula.

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

Where n is the number of items you can choose and choose r from them.

In this case $n = 12$ and $r = 5$

$12P5 =\frac{12!}{(12-5)!}$

$12P5 =\frac{12!}{7!}$

$12P5 =95040$