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A restaurant offers three courses, appetizers, main dishes and desserts. It has 6 choices of appetizers, 10 choices of main dishes and 8 choices of desserts. How many different meals are there if a customer can order only one dish from each course and can have a meal consisting of one course only, two different courses or a meal with all three courses.

2 Answers

2 votes

Answer:

692

Explanation:

User Ashark
by
7.3k points
5 votes

Answer:

692 different meals are possible.

Explanation:

- There are 3 courses, appetizers, main dishes and desserts.

- There are 6 choices of appetizers, 10 choices of main dishes and 8 choices of desserts.

- A customer can order only one dish from each course and can have a meal consisting of one course only, two different courses or a meal with all three courses.

To find the number of different meals possible, we take the choice of number of courses one by one.

- If a customer decides to take a meal with only one course.

The customer can take only 1 choice out of 6 choices of appetizers or 1 choice out of 10 choices of main dishes or 1 choice out of 8 choices of desserts.

6C1 + 10C1 + 8C1 = 6 + 10 + 8

= 24 different meals

- If a customer decides on a two course meal

The customer can combine a choice of appetizer with a choice of main dish or a choice of appetizer with desert or a choice of main dish with dessert with order unimportant.

(6C1 × 10C1) + (6C1 × 8C1) + (10C1 × 8C1)

= (6 × 10) + (6 × 8) + (10 × 8)

= 60 + 48 + 80

= 188 different meals

- If a customer decides to take a combination of all the 3 courses.

This means a combination of a choice from each of the courses for the 3 courses.

6C1 × 8C1 × 10C1

= 6 × 8 × 10

= 480 different meals.

Total number of different meals possible

= 24 + 188 + 480

= 692 different meals.

Hope this Helps!!!

User Bastes
by
7.2k points