9) A counting enthusiast goes to eat at the local diner. The 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. The enthusiast is on the latest fad diet, so they'l have to choose between a dessert and an appetizer. (They cannot have both.) Given this restriction, how many three-course meals are possible? Show all steps/work.
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
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