Homework, Page 708

1. Homework, Page 708 Count the number of ways that each procedure can be done. 1. Line up three people for a photograph.

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. Homework, Page 708 9. How many distinguishable 11-letter words may be made from the letters in MISSISSIPPI?

4. Homework, Page 708 Evaluate each expression without a calculator, then check. 13.

5. Homework, Page 708 Evaluate each expression without a calculator, then check. 17.

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. 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. 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. 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. 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. Homework, Page 708 41. How many different answer keys are possible for a ten question true - false test?

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. 9.2 The Binomial Theorem

14. Quick Review

15. Quick Review Solutions

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. Binomial Coefficient

18. Example Using nCr to Expand a Binomial

19. Pascal’s Triangle • Pascal’s Triangle is a listing of the coefficients of the terms in the expansion of a binomial.

20. Example Using Pascal’sTriangle to Expand a Binomial

21. The Binomial Theorem

22. Expanding a Binomial Points to note about Binomial Expansions: • The number of terms in the expansion is one more than the exponent. • 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. • The coefficient of the second term is the same as the exponent.

23. Example Evaluating a Coefficient in a Binomial Expansion by Hand

24. Example Writing the Specified Term of a Binomial Expansion

25. Basic Factorial Identities

26. Homework • Homework Assignment #28 • Review Section 9.2 • Page 715, Exercises: 1 – 37 (EOO) • Quiz next time

27. 9.3 Probability

28. Quick Review

29. Quick Review Solutions

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. Probability of an Event (Equally Likely Outcomes)

32. Probability Distribution for the Sum of Two Fair Dice Outcome Probability 2 1/36 3 2/36 4 3/36 5 4/36 6 5/36 7 6/36 8 5/36 9 4/36 10 3/36 11 2/36 12 1/36

33. Example Rolling the Dice Find the probability of rolling a sum divisible by 4 on a single roll of two fair dice.

34. Probability Function

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. Probability of an Event (Outcomes not Equally Likely)

37. Example Rolling the Dice Find the probability of rolling a sum divisible by 3 on a single roll of two fair dice.

38. Strategy for Determining Probabilities

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. Multiplication Principle of Probability Suppose an event A has probability p1 and an event B has probability p2 under the assumption that A occurs. Then the probability that both A and B occur is p1p2.

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. Conditional Probability Formula

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. Binomial Distribution

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. 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?