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Mr. Garcia always dresses in a shirt, slacks, and dress shoes. There are 64 different outfits he can make with them. If he has 8 shirts and 2 pairs of shoes, then how many pairs of slacks does he have?

Respuesta :

Stryfer

Answer:

4

Step-by-step explanation:

To find the total possibilities, you multiply the number of each decision you can make.  So, [tex]64=2*8*x\\16x=64\\x=4[/tex]

Using the Fundamental Counting Theorem, it is found that he has 4 pairs of slacks.

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:

  • There are 64 outfits, hence N = 64.
  • There are 8 shirts, hence [tex]n_1 = 8[/tex].
  • There are 2 pairs of shoes, hence [tex]n_2 = 2[/tex].
  • The number of pairs of slacks is [tex]n_3[/tex].

Then:

[tex]8 \times 2 \times n_3 = 64[/tex]

[tex]n_3 = \frac{64}{16}[/tex]

[tex]n_3 = 4[/tex]

He has 4 pairs of slacks.

To learn more about the Fundamental Counting Theorem, you can take a look at https://brainly.com/question/24314866

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