Respuesta :
Using the Fundamental Counting Theorem, it is found that the flags can be displayed in 518,400 ways.
What is the Fundamental Counting Theorem?
It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
In this problem, we have that odd positions get South American countries, hence:
[tex]n_1 = 6, n_3 = 5, n_4 = 3, \cdots, n_11 = 1[/tex]
Even positions get European countries, hence:
[tex]n_2 = 6, n_4 = 5, \cdots, n_12 = 1[/tex]
Hence, since the number of ways for both the South American and European countries is the factorial of 6, we have that:
N = 6! x 6! = 518,400
The flags can be displayed in 518,400 ways.
More can be learned about the Fundamental Counting Theorem at https://brainly.com/question/24314866
