Let's solve each of the four pizza ordering problems using the
Fundamental Counting Principle. This principle states that if there are multiple independent choices to be made, the total number of possible outcomes is the
product of the number of options for each choice.
---
Problem 1: Mia's Pizza Choice
> There are:
- 8 different toppings
- 4 different types of sauce
Assuming Mia chooses
one topping and
one sauce, then:
$$
\text{Total pizzas} = \text{Number of toppings} \times \text{Number of sauces}
= 8 \times 4 = 32
$$
✔ Answer: 32 different pizzas
---
Problem 2: Amira and Nico's Pizza Choice
> They can choose from:
- 2 different sizes
- 10 different toppings
- 5 different crusts
Assuming they pick
one size,
one topping, and
one crust:
$$
\text{Total pizzas} = 2 \times 10 \times 5 = 100
$$
✔ Answer: 100 different pizzas
---
Problem 3: You and Your Friend's Pizza Choice
> The store offers:
- 3 different sizes
- 4 different crusts
- 9 flavors of pizza
Assuming one choice per category:
$$
\text{Total pizzas} = 3 \times 4 \times 9 = 108
$$
✔ Answer: 108 different pizzas
---
Problem 4: Edrick and Friends' Pizza Choice
> They saw:
- 5 different sizes
- 3 different shapes
- 4 different crusts
- 7 flavors of pizza
All these are independent choices:
$$
\text{Total pizzas} = 5 \times 3 \times 4 \times 7 = 420
$$
✔ Answer: 420 different pizzas
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✔ Final Answers:
1.
32 different pizzas
2.
100 different pizzas
3.
108 different pizzas
4.
420 different pizzas
---
📌 Explanation Summary:
Each problem uses the
Fundamental Counting Principle:
> Multiply the number of choices in each category to get the total number of combinations.
This works because each choice is
independent — choosing a size doesn’t affect the number of available crusts or flavors.
Let me know if you'd like this explained with tree diagrams or visual models! 🍕
Parent Tip: Review the logic above to help your child master the concept of fundamental counting principle worksheet.
