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15.1 Permutations

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.

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15.1 Permutations

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  1. 15.1 Permutations Brett Solberg AHS ‘11-’12

  2. Warm-up • Simplify • 1) • 2) • Multiply • 3) (x – 1)3

  3. Today’s Agenda • Probability • Compound Events • Permutations • Ordered probability • Combinations • Unordered Probability • CRT Checklist • calculator • book • pencil

  4. 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?

  5. 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

  6. 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

  7. 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

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

  9. Permutations • Used for arranging a set of objectswhere order matters. • n = number of objects to choose from • r = number of objects to be arranged

  10. Examples • In how many ways can six circus elephants be arranged in a line? • In how many ways can the four symbols *, !, @, # be arranged?

  11. 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?

  12. 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.

  13. 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.

  14. Combination • n = number of objects • r = how many we choose

  15. Combinations

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

  17. Combination Example • In how many ways can a starting 11 unit be chosen from RSL’s 26 person roster?

  18. Combination Example • In how many ways can a committee of 3 be chosen from a group of 7 people?

  19. 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

  20. Assignments • 15.1 1 – 39 odd • 15.3 1 – 15 all

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