Download - Copyright 2009 Pearson Education, Inc. Chapter 12 Section 9 - Slide 1 P-9 Probability Combinations
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Copyright © 2009 Pearson Education, Inc. Chapter 12 Section 9 - Slide 1
P-9 Probability
Combinations
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Chapter 12 Section 9 - Slide 2Copyright © 2009 Pearson Education, Inc.
WHAT YOU WILL LEARN• How to solve combinations
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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 !
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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
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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
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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
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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.
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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
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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
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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
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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
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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
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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
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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
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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