Question

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

Answer 1

95,040 different cast are possible

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 =(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 =(12!)/((12-5)!)`

`12P5 =(12!)/(7!)`

`12P5 =95040`