Answer:
There are 220 different ways to arrange the acts.
Step-by-step explanation:
The order in which the acts are arranged is not important, so we use the combinations formula to solve this question.
Combinations Formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
How many different ways can the program manager arrange 3 different acts from the original 12
Three acts from a set of 12. So
[tex]C_{12,3} = \frac{12!}{3!(12-9)!} = 220[/tex]
There are 220 different ways to arrange the acts.
