At a restaurant, dinner guests can choose between two appetizers – soup or salad, three main dishes – chicken, pasta, or salmon, and two desserts – cake or pie. If customers do not want any dessert, they can get a second appetizer instead. (In this case, they can choose to get the same appetizer twice or two different appetizers.) How many different options are there for dinner at this restaurant? using branches for soup and salad
First, let's break down the options for each course:
Appetizers: soup or salad
Main dishes: chicken, pasta, or salmon
Desserts: cake or pie
If customers choose soup as their appetizer:
- They can choose chicken, pasta, or salmon as their main dish
- They can choose to have cake or pie for dessert
If customers choose salad as their appetizer:
- They can choose chicken, pasta, or salmon as their main dish
- They can choose to have cake or pie for dessert
If customers choose to have a second appetizer instead of dessert:
- They can choose either soup or salad as their second appetizer
Let's calculate the total number of options using branches for soup and salad:
For soup:
3 main dishes x 2 dessert options = 6 options
+ 1 option for a second appetizer instead of dessert
= 7 options for soup
For salad:
3 main dishes x 2 dessert options = 6 options
+ 1 option for a second appetizer instead of dessert
= 7 options for salad
Total options = 7 (soup) + 7 (salad) = 14 options
Therefore, there are 14 different options for dinner at this restaurant.