Using the Fundamental Counting Theorem, it is found that the buyer has 180 choices.
Fundamental counting theorem:
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 question:
- The options are independent.
- There are 5 different exterior colors, hence [tex]n_1 = 5[/tex].
- There are 3 different interior colors, hence [tex]n_2 = 3[/tex].
- There are 2 sound systems, hence [tex]n_3 = 2[/tex].
- There are 3 motor designs, hence [tex]n_4 = 3[/tex].
- There are 2 transmission options, hence [tex]n_5 = 2[/tex].
Then:
[tex]N = 5 \times 3 \times 2 \times 3 \times 2 = 180[/tex]
The buyer has 180 choices.
To learn more about the Fundamental Counting Theorem, you can take a look at https://brainly.com/question/25799621
