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How many ways can two teachers, four male students, five female students and one administrator be arranged if the teachers must sit together, the male students must sit together and the female students must sit together?

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

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