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Samantha is trying to pick out an outfit for the first day of school. She can choose from 2 pairs of pants, 2 t-shirts, and 9 pairs of shoes. How many different outfits does Samantha have to choose from?

Respuesta :

Using the Fundamental Counting Theorem, it is found that Samantha has 36 different outfits to choose from.

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:

  • For the pants, there are 2 options, hence [tex]n_1 = 2[/tex].
  • For the t-shirts, there are 2 outcomes, hence [tex]n_2 = 2[/tex].
  • For the shoes, there are 9 outcomes, hence [tex]n_3 = 9[/tex].

Thus, the total number of outfits is given by:

N = 2 x 2 x 9 = 36.

More can be learned about the Fundamental Counting Theorem at https://brainly.com/question/24314866

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