You and a friend are at Paul and Elizabeth's Restaurant for a night of fine dining. You can choose among 2 appetizers, 4 main dishes, and 3 desserts. Appetizer: soup or salad Main Dish: fish, chicken, beef, vegetarian Dessert: chocolate cake, apple pie, ice cream (a) How many possible different dinners are there? dinners (b) If there are 3 choices of salad dressing and 2 choices of ice cream, how many possible dinner combinations are there? dinner combinations
You and a friend are at Paul and Elizabeth's Restaurant for a night of fine dining. You can choose among 2 appetizers, 4 main dishes, and 3 desserts. Appetizer: soup or salad Main Dish: fish, chicken, beef, vegetarian Dessert: chocolate cake, apple pie, ice cream (a) How many possible different dinners are there? dinners (b) If there are 3 choices of salad dressing and 2 choices of ice cream, how many possible dinner combinations are there? dinner combinations
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
You and a friend are at Paul and Elizabeth's Restaurant for a night of fine dining. You can choose among 2 appetizers, 4 main dishes, and 3 desserts.
Appetizer: soup or salad
Main Dish: fish, chicken, beef, vegetarian
Dessert: chocolate cake, apple pie, ice cream
(a)
How many possible different dinners are there?
dinners
(b)
If there are 3 choices of salad dressing and 2 choices of ice cream, how many possible dinner combinations are there?
dinner combinations
Expert Solution
Step 1
We assume that a dinner constitutes of one appetizer, one main dish and one dessert.
(a) One appetizer can be chosen from the available two appetizers in 2C1 = 2 different ways.
One main dish can be chosen from the available four main dishes in 4C1 = 4 different ways.
One dessert can be chosen from the available three desserts in 3C1 = 3 different ways.
So, number of possible different dinner combinations = 2 × 4 × 3
= 24 [Ans]
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