The local diner offers a meal combination consisting of an appetizer, a soup, a main course, and a dessert. There are four appetizers, five soups, five main courses, and four desserts. Your diet restricts you to choosing between a dessert and an appetizer. (You cannot have both.) Given this restriction, how many three-course meals are possible

200 three-course meals are possible

Step-by-step explanation:

You are going to choose:

One soup, from a set of 5.

One main course, from a set of 5.

Either an appetizers or a dessert, from a set of 4+4 = 8

Total

5*5*8 = 200

200 three-course meals are possible

A total of 200 different three-course meals.

Step-by-step explanation:

1. Let's review the information provided to us to answer the question correctly:

Number of appetizers = 4

Number of soups = 5

Number of main courses = 5

Number of desserts = 4

Diet restrictions you need to choose between a dessert and an appetizer. (You cannot have both.)

2. Given this restriction, how many three-course meals are possible.

Let's find the number of possible three-meals with appetizers, as follows:

4 appetizers * 5 soups * 5 main courses = 100

Now, let's find the possible three-meals with desserts:

5 soups * 5 main courses * 4 desserts = 100

Because they're mutually exclusive, we sum for a total of 200 different three-course meals.