The supreme choice pizza at Pete's Pizza contains 3 different meats and 2 different vegetables.  The customer can select any one of 5 types of crust.  If there are 5 meats and 9 vegetables to choose from, how many different supreme choice pizzas can be made?

We can break down the problem by considering the choices step by step.

### Step 1: Selecting the meats
- There are 5 available meats, and the customer can choose 3 of them.
- The number of ways to choose 3 meats from 5 is a combination problem, given by:
\[
\binom{5}{3} = \frac{5!}{3!(5-3)!} = \frac{5 \times 4 \times 3!}{3! \times 2!} = \frac{5 \times 4}{2} = 10
\]

### Step 2: Selecting the vegetables
- There are 9 available vegetables, and the customer can choose 2 of them.
- The number of ways to choose 2 vegetables from 9 is another combination problem:
\[
\binom{9}{2} = \frac{9!}{2!(9-2)!} = \frac{9 \times 8}{2} = 36
\]

### Step 3: Selecting the crust
- The customer can choose 1 of 5 types of crust. So, there are 5 choices for the crust.

### Step 4: Total number of different pizzas
To find the total number of different pizzas, we multiply the number of ways to choose the meats, vegetables, and crust:
\[
\text{Total pizzas} = \binom{5}{3} \times \binom{9}{2} \times 5 = 10 \times 36 \times 5 = 1800
\]

Thus, the total number of different supreme choice pizzas that can be made is **1,800**.

Would you like more details on any part of the solution?

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Here are 5 related questions:
1. How would the total number of pizzas change if the customer could only choose 2 meats?
2. What if the customer could select 4 vegetables instead of 2?
3. How many pizzas could be made if only 3 crust options were available?
4. How does changing the number of available vegetables (from 9 to 10) affect the total choices?
5. What is the probability of randomly selecting a pizza with a specific combination of 1 meat, 1 vegetable, and 1 crust?

**Tip:** When solving combination problems, remember that order does not matter unless the question specifies otherwise.

The supreme choice pizza at Pete's Pizza contains 3 different meats and 2 different vegetables. The customer can select any one of 5 types of crust. If there are 5 meats and 9 vegetables to choose from, how many different supreme choice pizzas can be made?

Discover how to calculate the number of supreme choice pizzas with 3 different meats, 2 vegetables, and 5 crust options. This problem involves using combination formulas and is suitable for students in Grades 8-10. Learn step-by-step how to find the total of 1,800 possible pizza combinations.

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