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The local diner offers a meal combination consisting of an appetizer, a soup, a main course, and a dessert. There are three appetizers, five soups, three main courses, and three desserts. Your diet restricts you to choosing between a dessert and an appetizer. (You cannot have both.) Given this restriction, how many three-course meals are possible

User Yogi Joshi
by
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2 Answers

4 votes

Answer:

90?

Explanation:

User Autoplectic
by
7.1k points
5 votes

Answer:

number of ways to chose a three course meal is 90

Explanation:

Given the data in the question;

Number of appetizer = 3

Number of soups = 5

Number of main courses = 3

Number of desserts = 3

Now,

Number of ways that appetizer can be chosen = ³C₁ = 3!/(1!(3-1)!) = 3

Number of ways that soups can be chosen = ⁵C₁ = 5!/(1!(5-1)!) = 5

Number of ways that main courses can be chosen = ³C₁ = 3!/(1!(3-1)!) = 3

Number of ways that desserts can be chosen = ³C₁ = 3!/(1!(3-1)!) = 3

So,

First we chose an appetizer, soup and main course.

Number of ways will be;

⇒ 3 × 5 × 3 = 45

Next, we chose a dessert, a soup & a main course.

Number of ways will be;

⇒ 3 × 5 × 3 = 45

Total number of ways to chose a three course meal

⇒ 45 + 45 = 90 ways

Therefore, number of ways to chose a three course meal is 90

User Denis Valeev
by
8.9k points
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