Respuesta :
Using the Fundamental Counting Theorem, it is found that there are 160 ways for them to be arranged.
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]
For this problem, we have that the parameters are found as follows:
- There are four roles, hence [tex]n_1 = 4[/tex].
- There are two teachers, hence [tex]n_2 = 2[/tex].
- There are four male students, hence [tex]n_3 = 4[/tex].
- There are five female students, hence [tex]n_4 = 5[/tex].
- There is one administrator, hence [tex]n_5 = 1[/tex].
Thus the number of ways in which they can be arranged is:
N = 4 x 2 x 4 x 5 x 1 = 160.
More can be learned about the Fundamental Counting Theorem at https://brainly.com/question/24314866
#SPJ1
