Counting and Probability: Word Problems

At Lotsa Pizza, you can build your own pizza with the choices below:

• Dough: Traditional, Wheat, Gluten-Free
• Sauce: Red, Spicy Red, Sweet Agave Red, Olive Oil, BBQ, Buffalo, Alfredo
• Cheese: Mozzarella, Fresh Mozzarella, Ricotta, Blue Cheese, Cheddar Jack, Shaved Parmesan, Vegan Cheese
• Proteins: $7$ kinds of meat.
• Veggies: $12$ veggie toppings.
• Finishers: $12$ spices/sauces.

Assuming each pizza has only $1$ of each category, how many different pizzas can be made?