How many different meals are available when you select an​ appetizer, an​ entrée, and a​ dessert?

Question

A restaurant offers a​ $12 dinner special that has 7 choices for an​ appetizer,13 choices for an​ entrée, and 3 choices for a dessert. How many different meals are available when you select an​ appetizer, an​ entrée, and a​ dessert?

Answer 1

Answer: 7x13x3=273

Explanation:

This is an example of the multiplication principle. Each of the 7 appetizers has 13 possible meal choices and each appetizer and meal combo has 3 possible dessert choices:

If we just consider two appetizer choices, two meal choices, and three different desserts, we have:

Appetizer 1, meal 1, dessert 1

Appetizer 1, meal 1, dessert 2

Appetizer 1, meal 1, dessert 3

Appetizer 1, meal 2, dessert 1

Appetizer 1, meal 2, dessert 2

Appetizer 1, meal 2, dessert 3

Appetizer 2, meal 1, dessert 1

Appetizer 2, meal 1, dessert 2

Appetizer 2, meal 1, dessert 3

Appetizer 2, meal 2, dessert 1

Appetizer 2, meal 2, dessert 2

Appetizer 2, meal 2, dessert 3

Which is 2x2x3 = 12 different meal choices. Using the same logic, if we now have 7 appetizers, 13 meals, and 3 desserts, we have 7x13x3 = 273 options.