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

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

P-9 Probability

Combinations

Chapter 12 Section 9 - Slide 2Copyright © 2009 Pearson Education, Inc.

WHAT YOU WILL LEARN• How to solve combinations

Chapter 12 Section 9 - Slide 3Copyright © 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

nCr

n!n r !r !

Chapter 12 Section 9 - Slide 4Copyright © 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.

7C4 7!

7 4 !4!

7!3!4!

76 5432132 14321

35

Chapter 12 Section 9 - Slide 5Copyright © 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?

Bread choices 5C2 4C2 3C1

1063180

Chapter 12 Section 10 - Slide 6Copyright © 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?

æ ö=ç ÷è ø

× × × × × × × × ×××× ×××= = = ××××× × ×××× ×× ×××

= =

6 2

11 4

two # of possible committees with 2 womantotal number of 4-member committeeswoman

6!6 5 4 3 2 1 7 6 5 4 3 2 1 4 3 2 14!2!

11! 4 3 2 1 2 1 11 10 9 8 7 6 5 4 3 2 17!4!

15 1330 22

P

CC

3

3

Chapter 12 Section 10 - Slide 7Copyright © 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 thata) no chocolate flavors are selected.b) at least 1 chocolate is selected.c) 2 vanilla and 2 chocolate are selected.

Chapter 12 Section 10 - Slide 8Copyright © 2009 Pearson Education, Inc.

Solution

5 vanilla, 3 chocolate, 2 strawberryselecting 4 flavors

a)

b)

P no chocolate 7C4

10C4

35210

16

P at least 1 chocolate 1 P no chocolate 1

16

56

Chapter 12 Section 10 - Slide 9Copyright © 2009 Pearson Education, Inc.

Solution (continued)

5 vanilla, 3 chocolate, 2 strawberry;selecting 4 flavors

c.

P2 vanilla and2 chocolate

5C2 3C2

10C4

103210

30210

17

Slide 12 - 10Copyright © 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.

1

16 29480

b.

d. 14

29476

Slide 12 - 11Copyright © 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.

1

16 29480

b.

d. 14

29476

Slide 12 - 12Copyright © 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.

1516

447476

b.

d. 9

16 38

Slide 12 - 13Copyright © 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.

1516

447476

b.

d. 9

16 38

Slide 12 - 14Copyright © 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

Slide 12 - 15Copyright © 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