Answer:
900,900 outcomes are possible.
Step-by-step explanation:
Arrangements with repetition:
The number of possible arrangements of n elements, considered that they are divided in classes of [tex]n_1,n_2,...,n_n[/tex] elements, is given by:
[tex]A = \frac{n!}{n_1!n_2!...n_n!}[/tex]
A dancing competition has 13 competitors
This means that [tex]n = 13[/tex]
Four are American, two are Mexicans, four are Russians and three are Italians.
This means that [tex]n_1 = 4, n_2 = 2, n_3 = 4, n_4 = 3[/tex]
How many outcomes are possible?
[tex]A = \frac{13!}{4!2!4!3!} = 900900[/tex]
900,900 outcomes are possible.
