Permutations Lesson 10.1B.

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Presentation transcript:

Permutations Lesson 10.1B

Warm-ups You are ordering a one-topping pizza. If you can choose between small, medium or large, thick or thin crust, pepperoni, sausage, Canadian bacon, or vegetarian, and must decide whether you want extra cheese, how many pizzas are possible? Answer : 3 x 2 x 4 x 2 = 48

no calculator b) 4! = 8! 7! = 6! 4!2! =

In how many ways can your seven classes be arranged? Answer: 7x6x5x4x3x2x1 = 7! = 5040

d) 5 kids in your family Mom wants one to spend Saturday morning having one doing laundry, another doing dishes, and a third cleaning the garage In how many different ways can she assign these chores? Answer : 5x4x3 = 60

When selecting r different objects from a group of n, they can be arranged in P(n,r) = nPr = 𝑛! 𝑛−𝑟 ! ways. For example when choosing 3 kids from 5, 5P3 = 5! 2! = 5X4X3 = 60 Why might we ever want to use this formula? The problem was pretty easy anyway. Why was the word arranged important?

Find each answer two or more ways. (Hint: 0! = 1 by definition) 6P2 = 7P4 = 8P1 = 8P8 = 8P0 =

You want to select 3 songs to play at the talent show from 10 that you know really well. In how many ways can you arrange your part of the program? Answer: 10P3 = 720