Mario's Pizza has 2 choices of crust: deep dish and thin - and crispy. The restaurant also has a choice of 5 toppings : tomatoes, sausage, pepeers, onions, and pepperoni. Finally, Mario's offers every pizza in extra cheese as well as regular. If Linda's volleyball team decides to order a pizza with 4 toppings, how many different choices do the teammates have at Mario's Pizza?

Answer

To solve the problem of how many different pizza choices Linda's volleyball team has at Mario's Pizza, we can break it down step by step.

### Step 1: Determine the number of ways to choose the toppings.
Linda's team wants to order a pizza with 4 toppings from a selection of 5 toppings: tomatoes, sausage, peppers, onions, and pepperoni.

To find out how many ways we can choose 4 toppings from 5, we use the combination formula:

\[ \text{Number of ways to choose } r \text{ items from } n \text{ items} = \binom{n}{r} = \frac{n!}{r!(n-r)!} \]

In this case, \( n = 5 \) (the total number of toppings) and \( r = 4 \) (the number of toppings to choose).

\[ \binom{5}{4} = \frac{5!}{4!(5-4)!} = \frac{5!}{4! \cdot 1!} = \frac{5 \times 4!}{4! \cdot 1} = 5 \]

So, there are 5 ways to choose 4 toppings from 5.

### Step 2: Determine the number of crust options.
Mario's Pizza offers 2 choices of crust: deep dish and thin and crispy.

Thus, the number of crust options is:

\[ \text{Number of crust options} = 2 \]

### Step 3: Determine the number of cheese options.
Mario's Pizza also offers 2 choices for cheese: extra cheese and regular.

Thus, the number of cheese options is:

\[ \text{Number of cheese options} = 2 \]

### Step 4: Calculate the total number of different pizza combinations.
To find the total number of different pizza combinations, we multiply the number of ways to choose the toppings by the number of crust options and the number of cheese options:

\[ \text{Total combinations} = (\text{Number of topping combinations}) \times (\text{Number of crust options}) \times (\text{Number of cheese options}) \]

Substituting the values we found:

\[ \text{Total combinations} = 5 \times 2 \times 2 = 20 \]

Thus, the total number of different choices Linda's volleyball team has at Mario's Pizza is **20**.

### Final Answer:
The total number of different pizza choices is **20**.

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