Using the Fundamental Counting Theorem, it is found that there are 576 ways for the dancers to line up.
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, considering the order:
Black - Red - Black - Red - Black - Red - Black - Red
The number of ways for each is given by:
4 - 4 - 3 - 3 - 2 - 2 - 1 - 2
Hence:
[tex]N = 4^2 \times 3^2 \times 2^2 = 576[/tex]
There are 576 ways for the dancers to line up.
To learn more about the Fundamental Counting Theorem, you can check https://brainly.com/question/24314866
