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!!!