1. Copyright © 2009 Pearson Education, Inc. Chapter 12 Section 9 - Slide 1 P-9 Probability Combinations

2. Chapter 12 Section 9 - Slide 2 Copyright © 2009 Pearson Education, Inc. WHAT YOU WILL LEARN How to solve combinations

3. Chapter 12 Section 9 - Slide 3 Copyright © 2009 Pearson Education, Inc. Combination A combination is a distinct group (or set) of objects without regard to their arrangement. The number of combinations possible when r objects are selected from n objects is found by

4. Chapter 12 Section 9 - Slide 4 Copyright © 2009 Pearson Education, Inc. Example A student must select 4 of 7 essay questions to be answered on a test. In how many ways can this selection be made? There are 35 different ways that 4 of 7 questions can be selected.

5. Chapter 12 Section 9 - Slide 5 Copyright © 2009 Pearson Education, Inc. Example Toastline Bakery is testing 5 new wheat breads, 4 bran breads and 3 oat breads. If it plans to market 2 of the wheat breads, 2 of the bran breads and one of the oat breads, how many different combinations are possible?

6. Chapter 12 Section 10 - Slide 6 Copyright © 2009 Pearson Education, Inc. Example A club consists of 5 men and 6 women. Four members are to be selected at random to form a committee. What is the probability that the committee will consist of two women? 3 3

7. Chapter 12 Section 10 - Slide 7 Copyright © 2009 Pearson Education, Inc. Example The Honey Bear is testing 10 new flavors of ice cream. They are testing 5 vanilla based, 3 chocolate based and 2 strawberry based ice creams. If we assume that each of the 10 flavors has the same chance of being selected and that 4 new flavors will be produced, find the probability that a) no chocolate flavors are selected. b) at least 1 chocolate is selected. c) 2 vanilla and 2 chocolate are selected.

8. Chapter 12 Section 10 - Slide 8 Copyright © 2009 Pearson Education, Inc. Solution 5 vanilla, 3 chocolate, 2 strawberry selecting 4 flavors a) b)

9. Chapter 12 Section 10 - Slide 9 Copyright © 2009 Pearson Education, Inc. Solution (continued) 5 vanilla, 3 chocolate, 2 strawberry; selecting 4 flavors c.

10. Slide 12 - 10 Copyright © 2009 Pearson Education, Inc. A box contains a total of 120 folders, of which 30 are red. If you select 2 at random, determine the probability that both folders are red. a. c. b. d.

11. Slide 12 - 11 Copyright © 2009 Pearson Education, Inc. A box contains a total of 120 folders, of which 30 are red. If you select 2 at random, determine the probability that both folders are red. a. c. b. d.

12. Slide 12 - 12 Copyright © 2009 Pearson Education, Inc. A box contains a total of 120 folders, of which 30 are red. If you select 2 at random, determine the probability that at least one folder is not red. a. c. b. d.

13. Slide 12 - 13 Copyright © 2009 Pearson Education, Inc. A box contains a total of 120 folders, of which 30 are red. If you select 2 at random, determine the probability that at least one folder is not red. a. c. b. d.

14. Slide 12 - 14 Copyright © 2009 Pearson Education, Inc. Ten green T-shirts and 6 orange T-shirts are placed in a box. Seven T-shirts are to be selected at random without replacement. Determine the probability that three green T- shirts and four orange T-shirts are selected. a.0.157 b.0.107 c.0.026 d.0.003

15. Slide 12 - 15 Copyright © 2009 Pearson Education, Inc. Ten green T-shirts and 6 orange T-shirts are placed in a box. Seven T-shirts are to be selected at random without replacement. Determine the probability that three green T- shirts and four orange T-shirts are selected. a.0.157 b.0.107 c.0.026 d.0.003