Warm Up Melanie is choosing an outfit for a job interview. She has four dresses, three shirts, five pairs of pants and three pairs of shoes to choose.

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Presentation transcript:

Warm Up Melanie is choosing an outfit for a job interview. She has four dresses, three shirts, five pairs of pants and three pairs of shoes to choose from. How many possible outfits can Melanie wear?

Answer Melanie is choosing an outfit for a job interview. She has four dresses, three shirts, five pairs of pants and three pairs of shoes to choose from. How many possible outfits can Melanie wear? 57 outfits

Combinations

Combinations ORDER DOESN’T MATTER n is the number you are choosing from r is the number you want C =

Example 1 There are seven books on your summer reading list. How many ways can you choose five books to read?

9C4 “9 choose 4” Combination Notation Example: There are 9 colored pencils, and we are choosing 4 of them. Another notation you might see is:

Example 2 A magazine company has 20 subscriptions to choose from. In how many ways can you order 4 magazines?

Example 3: Your turn! Of the 20 books on your reading list, in how many ways can you choose 7 books? In how many ways can 3 pizza toppings be chosen from 12 available toppings? In how many ways can 7 students from a class of 30 be chosen for a field trip?

We’ve been considering one “event” at a time We’ve been considering one “event” at a time. However, we can use combinations with multiple events using the fundamental counting principle.

Example 3 Sal’s Pizza has a selection of 10 toppings, 16 cheeses, and 7 sauces. How many possible pizzas are there if you can choose 5 toppings, 4 cheeses, and 2 sauces? __________________ Event 1: Choose toppings. __________________ Event 2: Choose cheeses. __________________ Event 3: Choose sauces.

Solution 10C5 • 16C4 • 7C2 Answer: 9631440

Example 4: You try! Mary’s Bakery offers 40 different cupcakes, 24 different cookies, and 7 varieties of cannoli. For a party tray, customers can choose 15 cupcakes, 10 cookies and 5 cannoli. How many possible party trays are there?

Solution 40C15 • 24C10 • 7C5 Answer: 1.657 x 1018 Whoa.