Respuesta :
Answer:
192pizzas
Step-by-step explanation:
- To make your own pizza you would have to choose a type of meat, cheese, crust, sauces.
- Papa John's has the following number of choices for each step:
Types of meat = 8
Types of cheeses = 4
Types of crusts = 3
Types of sauces = 2
- We have to choose "1" type from each of the available 4 categories to complete our pizza.
- We will use selection process " combinations" to determine of ways we could make our own pizza:
Select 1 type meat = 8C1 = 8
Select 1 type of cheese = 4C1 = 4
Select 1 type of crust = 3C1 = 3
Select 1 type of sauce = 2C1 = 2
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Total ways to make a pizza = 8 * 4 * 3 * 2 = 192 ways
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- So we would have to choose from 192 different pizzas.
Using the Fundamental Counting Theorem, it is found that you have 192 different pizzas to choose from.
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 problem:
- For the meat, there are 8 options, hence [tex]n_1 = 8[/tex].
- For the cheese, there are 4 options, hence [tex]n_2 = 4[/tex].
- For the crust, there are 3 options, hence [tex]n_3 = 3[/tex].
- For the sauce, there are 2 options, hence [tex]n_4 = 2[/tex].
Then:
[tex]N = 8(4)(3)(2) = 192[/tex]
You have 192 different pizzas to choose from.
To learn more about the Fundamental Counting Theorem, you can take a look at https://brainly.com/question/24314866
