Question

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, five 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? choices

Answer 1

Answer:

Data given:

The local diner offers a meal combination consisting of an appetizer, a soup, a main course, and a dessert.

Number of options to choose from for appetizers = 3

Number of options to choose from for soups = 5

Number of options to choose from for main courses = 5

Number of options to choose from for desserts = 3

A person has a diet restriction of choosing between a dessert and an appetizer.

Now, using the above information, we can compute the total number of three-course meals possible (taking diet restriction into consideration) as -

1. If the person chooses appetizer, then-

Total number of three-course meals possible = (Number of ways of selecting 1 appetizer from 3 appetizers) x (Number of ways of selecting 1 soup from 5 soups) x (Number of ways of selecting 1 main course from 5 main courses)   

$= \ ^{3}C_{1} \times \ ^{5}C_{1} \times \ ^{5}C_{1}$

$= 3\times 5\times 5 = 75$

2. If the person chooses dessert, then-

Total number of three-course meals possible = (Number of ways of selecting 1 dessert from 3 desserts) x (Number of ways of selecting 1 soup from 5 soups) x (Number of ways of selecting 1 main course from 5 main courses)   

$= \ ^{3}C_{1} \times \ ^{5}C_{1} \times \ ^{5}C_{1}$

$= 3\times 5\times 5 = 75$

Therefore, the total number of three-course meals possible are 150 ( = 75 + 75) .