15.1 permutations

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15.1 Permutations

Brett Solberg AHS ‘11-’12

+Warm-up

Simplify 1) 2) Multiply 3) (x – 1)3

+Today’s Agenda

Probability Compound Events Permutations

Ordered probability Combinations

Unordered Probability

CRT Checklist calculator book pencil

+Texas Roadhouse

Steak + Salad + Side

Steak Salad Side 6 oz House Baked Potato 8 oz Caesar Fries 10 oz Chili

Event Dinner

Outcome What I eat

How many different outcomes are there?

+Fundamental Counting Principle

The total number of outcomes is all of the possibilities for each event multiplied together.

Steak + Salad + Side 3 * 2 * 4 24 total outcomes

+What to wear?

Jani can choose gray or blue jeans, a navy, white, green, or striped shirt, and running shoes, boots, or penny loafers. How many outfits can she wear?

Pants + shirt + shoes

+Pizza

A restaurant offers four sizes of pizza, two types of crust, and eight toppings. How many combinations with one topping are there?

Size + crust + topping

+Factorials!

A number multiplied by all numbers less than it. 5! = 5*4*3*2*1 9! 0! a!

+Permutations

Used for arranging a set of objects where order matters.

n = number of objects to choose from r = number of objects to be arranged

+Examples In how many ways can six circus elephants be arranged

in a line?

In how many ways can the four symbols *, !, @, # be arranged?

+Examples In how many ways can one write three letters on a tag

using the letter A, B, C, D, and E at most once.

A teacher wants to write an ordered 6-questions test from a pool of 10 questions. How many different forms of the test can the teacher write?

+Examples

How many 7-digit numbers can be named, without repetition, using the digits 2, 3, 4, 5, 6, 7, and 8 if an even digit must come first.

+Combination

Deals with ways of selecting from a set.

How many combinations are there of the set {A, B, C, D} taken two at a time? {A, B} {A, C} {A, D} {B, C} {B, D} {C, D}

How is this different from a permutation? Combination - selection is important, not order.

+Combination

n = number of objects r = how many we choose

+Combinations

+Combination Examples

In how many ways can a 5-player starting unit be selected from Alta’s 12 member basketball squad?

+Combination Example

In how many ways can a starting 11 unit be chosen from RSL’s 26 person roster?

+Combination Example

In how many ways can a committee of 3 be chosen from a group of 7 people?

+

You want to ride the following rides at Lagoon but only have time to ride 4. How many possibilities are there? Samurai Colossus Bombora Jet Star 2 Rocket Rattlesnake Rapids

+Assignments

15.1 1 – 39 odd 15.3 1 – 15 all