SWBAT apply the fundamental counting principle to solve counting problems

12.6 Counting Principle

You are traveling through Europe for the summer and decide the best

packing option is to select separates that can be mixed and

matched. You pack 1 pair of shorts and 1 pair of pants. You pack a pair of sandals and a pair of sneakers.

You also pack three shirts (red, blue, and white). How many

different outfits can be worn? Use a tree diagram to find the answer.

Problem 1

You are at an ice cream shop and have decided to have an ice cream sundae.

You have two options for size (regular or large). Five flavors of ice cream to

choose from (chocolate, vanilla, strawberry, cookie dough, or mint

chocolate chip). You also have 3 syrup toppings (hot fudge, caramel,

butterscotch) and 5 hard toppings (m&ms, peanut butter cups, gummy bears, nuts, sprinkles). How many

different possible sundaes could you make? Use a tree diagram to figure out

the answer.

Problem 2

The number of ways in which successive things can occur is

found by multiplying the number of ways each thing can occur.

Fundamental Counting Principle

A restaurant is rented for a retirement party. The owner offers an appetizer, an entree,

and a dessert for a set price. The following are the choices that people attending the

party may choose from. How many possible dinners could be served that night?

Appetizer: calamari, stuffed mushrooms, or Caesar salad

Entrees: tortellini alfredo, shrimp scampi, eggplant parmesan, or chicken marsala

Desserts: tiramisu or flan

Problem 1

In problem 1, the restaurant will lower the cost per person for the retirement party if the number of

appetizers and entrees is reduced. Suppose the appetizers are reduced

to either soup or salad and the entrees are reduced to either

tortellini or eggplant parmesan How many possible dinners could be

served at the party?

Problem 2

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