1. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 1 Homework, Page 708 Count the number of ways that each procedure can be done. 1.Line up three people for a photograph.

2. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 2 Homework, Page 708 5.There are four candidates for homecoming queen and three candidates for king. How many king-queen pairings are possible?

3. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 3 Homework, Page 708 9.How many distinguishable 11-letter words may be made from the letters in MISSISSIPPI?

4. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 4 Homework, Page 708 Evaluate each expression without a calculator, then check. 13.

5. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 5 Homework, Page 708 Evaluate each expression without a calculator, then check. 17.

6. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 6 Homework, Page 708 Tell whether permutations or combinations are being described. 21.Four students are selected from the senior class to form a committee to advise the cafeteria director about food. Combination

7. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 7 Homework, Page 708 25.Suppose that two dice, one red and one green are rolled. How many different outcomes are possible for the pair of dice?

8. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 8 Homework, Page 708 29.Juan has money to buy only three of the 48 CDs available. How many different sets of CDs can be purchased?

9. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 9 Homework, Page 708 33.Six seniors at Rydell High School meet the qualifications for a competitive honor scholarship at a major university. The university allows the school to nominate three candidates, and the school always nominates at least one. How many different choices could the nominating committee make?

10. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 10 Homework, Page 708 37.Mary’s lunch always consists of a full plate of salad from Ernestine’s salad bar. She always takes equal amounts of each salad she chooses, but she likes to vary her selections. If she can choose from among nine salads, how many essentially different lunches can she create?

11. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 11 Homework, Page 708 41.How many different answer keys are possible for a ten question true - false test?

12. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 12 Homework, Page 708 45.Lunch at the Gritsy Palace consists of an entrée, two vegetables, and a dessert. If there are four entrees, six vegetables, and six desserts from which to choose, how many essentially different lunches are possible? A.16 B.25 C.144 D. 360 E.720

13. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 9.2 The Binomial Theorem

14. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 14 Quick Review

15. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 15 Quick Review Solutions

16. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 16 What you’ll learn about Powers of Binomials Pascal’s Triangle The Binomial Theorem Factorial Identities … and why The Binomial Theorem is a marvelous study in combinatorial patterns.

17. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 17 Binomial Coefficient

18. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 18 Example Using n C r to Expand a Binomial

19. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 19 Pascal’s Triangle Pascal’s Triangle is a listing of the coefficients of the terms in the expansion of a binomial.

20. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 20 Example Using Pascal’s Triangle to Expand a Binomial

21. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 21 The Binomial Theorem

22. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 22 Expanding a Binomial Points to note about Binomial Expansions: 1.The number of terms in the expansion is one more than the exponent. 2.The sum of the exponents of the variables in a term is always the exponent to which the binomial is raised, assuming both variables are first order in the initial expression. 3.The coefficient of the second term is the same as the exponent.

23. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 23 Example Evaluating a Coefficient in a Binomial Expansion by Hand

24. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 24 Example Writing the Specified Term of a Binomial Expansion

25. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 25 Basic Factorial Identities

26. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 26 Homework Homework Assignment #28 Review Section 9.2 Page 715, Exercises: 1 – 37 (EOO) Quiz next time

27. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 9.3 Probability

28. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 28 Quick Review

29. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 29 Quick Review Solutions

30. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 30 What you’ll learn about Sample Spaces and Probability Functions Determining Probabilities Venn Diagrams and Tree Diagrams Conditional Probability Binomial Distributions … and why Everyone should know how mathematical the “laws of chance” really are.

31. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 31 Probability of an Event (Equally Likely Outcomes)

32. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 32 Probability Distribution for the Sum of Two Fair Dice OutcomeProbability 21/36 32/36 43/36 54/36 65/36 76/36 85/36 94/36 103/36 112/36 121/36

33. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 33 Example Rolling the Dice Find the probability of rolling a sum divisible by 4 on a single roll of two fair dice.

34. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 34 Probability Function

35. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 35 Example Testing the Validity of a Probability Function Is it possible to weight a standard number cube in such a way that the probability of rolling a number n is exactly 1/(n+2)?

36. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 36 Probability of an Event (Outcomes not Equally Likely)

37. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 37 Example Rolling the Dice Find the probability of rolling a sum divisible by 3 on a single roll of two fair dice.

38. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 38 Strategy for Determining Probabilities

39. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 39 Example Choosing Chocolates Dylan opens a box of a dozen chocolate cremes and offers three of them to Russell. Russell likes vanilla cremes the best, but all the chocolates look alike on the outside. If five of the twelve cremes are vanilla, what is the probability that all of Russell’s picks are vanilla?

40. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 40 Multiplication Principle of Probability Suppose an event A has probability p 1 and an event B has probability p 2 under the assumption that A occurs. Then the probability that both A and B occur is p 1 p 2.

41. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 41 Venn Diagram Venn diagrams are visual representations of groupings of events. E.g., if 63% of the students are girls and 54% of the students play sports, find the percentage of boys playing sports if 1/3 of the girls play sports.

42. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 42 Conditional Probability Formula

43. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 43 Example Using the Conditional Probability Formula Two identical cookie jars are on a counter. Jar A contains eight cookies, six of which are oatmeal, and jar B contains four cookies, two of which are oatmeal. If an oatmeal cookie is selected, what is the likelihood it came from the jar A?

44. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 44 Binomial Distribution

45. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 45 Example Shooting Free Throws Suppose Tommy makes 92% of his free throws. If he shoots 15 free throws, and if his chance of making each one is independent of the other shots, what is the probability that he makes all 15?

46. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 9- 46 Example Shooting Free Throws Suppose Tommy makes 92% of his free throws. If he shoots 15 free throws, and if his chance of making each one is independent of the other shots, what is the probability that he makes exactly 10?