The local dinner offers a meal combination consisting of an appetizer, two soups, four main courses, and five desserts. Your diet retricts you to choosing between a dessert and an appetizer. (You cannot have both). Given this restriction, how many three-course meals are possible?
To find the number of three-course meals possible with the given restriction, we can consider all the possible combinations of an appetizer, a main course, and either a soup or a dessert.
First, let's consider the options for the appetizer. We have one option since we can only choose between an appetizer and a dessert.
Next, let's consider the options for the main course. We have four options to choose from.
Finally, let's consider the options for the soup or dessert. We have two options since we can only choose between a soup and a dessert.
By multiplying the number of options for each course together, we can find the total number of three-course meals possible:
1 (option for appetizer) x 4 (options for main course) x 2 (options for soup or dessert) = 8
Therefore, there are 8 possible three-course meals with the given restriction.
To find the number of three-course meals possible, we need to consider the possible combinations of an appetizer, main course, and dessert.
Since you are restricted to choosing either a dessert or an appetizer, we have two cases to consider:
Case 1: Choosing a dessert
In this case, we need to choose one appetizer and one main course from the available options. We can choose one dessert in 5 ways, one appetizer in 1 way, and one main course in 4 ways.
So, the number of three-course meals when choosing a dessert is 5 * 1 * 4 = 20.
Case 2: Choosing an appetizer
Similarly, when choosing an appetizer, we need to select one dessert and one main course. We can choose one appetizer in 1 way, one dessert in 4 ways, and one main course in 4 ways.
So, the number of three-course meals when choosing an appetizer is 1 * 4 * 4 = 16.
Now, to get the total number of three-course meals possible, we need to sum up the results from both cases:
Total number of three-course meals = Number of meals when choosing a dessert + Number of meals when choosing an appetizer
= 20 + 16
= 36.
Therefore, there are 36 possible three-course meals when restricted to choosing between a dessert and an appetizer.