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
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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
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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 2C= 2 different ways. 

    One main dish can be chosen from the available four main dishes in 4C= 4 different ways. 

    One dessert can be chosen from the available three desserts in 3C= 3 different ways. 

    So, number of possible different dinner combinations = 2 × 4 × 3

                          = 24 [Ans]

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