Possible meals you can get
A restaurant offers 5 choices of appetizer, 10 choices of the main course and 4 choices of dessert. A customer can choose to eat just one course, or two different courses, or all three courses. Assuming that all food choices are available, how many different possible meals does the restaurant offer?
Note: When you eat a course, you only pick one of the choices.
The answer is 329.
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A person who eats only an appetizer has 5 choices. A person who eats only a main meal has 10 choices. A person who eats only a dessert has 4 choices.
A person who eats an appetizer and a main meal has 5 × 10 = 50 choices. A person who eats an appetizer and a dessert has 5 × 4 = 20 choices. A person who eats a main meal and a dessert has 10 × 4 = 40 choices.
A person who eats all three courses has 5 × 10 × 4 = 200 choices
So the total number of possible meals = 5 + 10 + 4 + 50 + 20 + 40 + 200 = 329
Here is another way to calculate it:
Including "none" as an option, there are 6 choices of appetizer, 11 choices of main meal and 5 choices of dessert. Thus the total number of choices is 6 × 11 × 5 = 330.
One of these is not a meal though (no appetizer, no main meal and no dessert), so there are 329 possible meals.