Question

We have seen combinatorial problems in a few places now, including India. Solve the following problem: You arrive at a restaurant and sit down with the menu. There are 3 appetizers, 3 salads, 5 entrees, and 4 desserts. How many meals (combinations of appetizer, salad, entrée and dessert) can you make? You may use any method you wish, but you must show how you arrived at the answer.

Answer 1

You can make 180 meals.

Explanation:

We can look at this problem the following way:

For each appetizers, we can choose 3 salads.

For each salad, we can choose 5 entrees. So we already have 3 salads, each with 5 possible entrees, so there are already 3*5 = 15 possibilities.

For each entree, we can choose 4 desserts. So for each of the 15 possibilites of salad and entrees, there are 4 desserts. So there are 15*4 = 60 possibilities.

There are also 3 appetizers possible for each of the 60 possibilities of salads, entrees and desserts. So there are 60*3 = 180 possibilities.