The local diner offers a meal combination consisting of an a

The local diner offers a meal combination consisting of an appetizer, a soup, a main course, and a dessert. There are three appetizers, four 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?

Solution

Number of appetizers = 3
Number of soups = 4
Number of main course= 5
Number of desserts= 3

Appetizer can be chosen in 3C1 = 3 ways
Soup can be chosen in 4C1 = 4 ways
A main course can be chosen in 5C1 = 5 ways
A dessert can be chosen in 3C1 = 3 ways.

First we chose an appetizer , a soup & main course.
Number of ways = 3 × 4 × 5 = 60
Now we chose a dessert, a soup & a main course.
Number of ways = 4 × 5 × 3 = 60
Total number of ways to chose a three course meal = 60 + 60 = 120 ways.

Answer : 120 three course meals are possible.