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Chapter 12: Rational Expressions & Functions 12.8 Combinations.
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Transcript of Chapter 12: Rational Expressions & Functions 12.8 Combinations.
![Page 1: Chapter 12: Rational Expressions & Functions 12.8 Combinations.](https://reader036.fdocuments.us/reader036/viewer/2022082518/56649ef05503460f94c00488/html5/thumbnails/1.jpg)
Chapter 12: Rational Expressions & Functions
12.8Combinations
![Page 2: Chapter 12: Rational Expressions & Functions 12.8 Combinations.](https://reader036.fdocuments.us/reader036/viewer/2022082518/56649ef05503460f94c00488/html5/thumbnails/2.jpg)
Permutations vs Combinations
• Permutations have a specific order– My sandwich needs to be bread, cheese, meat,
bread
• Combinations can be any order– My sandwich can be in any order, just has to have
two slices of bread, meat, and cheese
![Page 3: Chapter 12: Rational Expressions & Functions 12.8 Combinations.](https://reader036.fdocuments.us/reader036/viewer/2022082518/56649ef05503460f94c00488/html5/thumbnails/3.jpg)
Finding Combinations
rr
rnrn P
PC
![Page 4: Chapter 12: Rational Expressions & Functions 12.8 Combinations.](https://reader036.fdocuments.us/reader036/viewer/2022082518/56649ef05503460f94c00488/html5/thumbnails/4.jpg)
Example 1
37
24
58
C
C
C
![Page 5: Chapter 12: Rational Expressions & Functions 12.8 Combinations.](https://reader036.fdocuments.us/reader036/viewer/2022082518/56649ef05503460f94c00488/html5/thumbnails/5.jpg)
Example 2
• Twenty people report for jury duty. How many different twelve-person juries can be chosen?
![Page 6: Chapter 12: Rational Expressions & Functions 12.8 Combinations.](https://reader036.fdocuments.us/reader036/viewer/2022082518/56649ef05503460f94c00488/html5/thumbnails/6.jpg)
Example 2a
• For your history report, you can choose to write about two of a list of five presidents of the United States. Find the number of combinations possible for your report.
• Explain why you should model this situation with combinations, not permutations.
![Page 7: Chapter 12: Rational Expressions & Functions 12.8 Combinations.](https://reader036.fdocuments.us/reader036/viewer/2022082518/56649ef05503460f94c00488/html5/thumbnails/7.jpg)
Example 3
• Suppose you have six new CDs (two rock, two R&B, and two jazz) to put on a rack. If you choose the CDs are random, what is the probability that the first one is jazz and the second one is R&B?
![Page 8: Chapter 12: Rational Expressions & Functions 12.8 Combinations.](https://reader036.fdocuments.us/reader036/viewer/2022082518/56649ef05503460f94c00488/html5/thumbnails/8.jpg)
Example 3a
• Suppose you have three novels and two history books to read over the summer. If you choose these books at random, what is the probability that you first choose a novel, and then a history book?
![Page 9: Chapter 12: Rational Expressions & Functions 12.8 Combinations.](https://reader036.fdocuments.us/reader036/viewer/2022082518/56649ef05503460f94c00488/html5/thumbnails/9.jpg)
Rewrite probability as combinations
rt
rf
C
C
total
favorableeventP )(
![Page 10: Chapter 12: Rational Expressions & Functions 12.8 Combinations.](https://reader036.fdocuments.us/reader036/viewer/2022082518/56649ef05503460f94c00488/html5/thumbnails/10.jpg)
Example 4
• Suppose you have six Virginia quarters and four Connecticut quarters in a change purse. You choose three quarters without looking. What is the probability that all the quarters you choose are Virginia quarters?
![Page 11: Chapter 12: Rational Expressions & Functions 12.8 Combinations.](https://reader036.fdocuments.us/reader036/viewer/2022082518/56649ef05503460f94c00488/html5/thumbnails/11.jpg)
Example 4a
• Suppose you have the quarters in Example 4. You choose four quarters at random. How many combinations are possible?
• How many combinations are only Connecticut?
• What is the probability that all of the quarters are Virginia?
![Page 12: Chapter 12: Rational Expressions & Functions 12.8 Combinations.](https://reader036.fdocuments.us/reader036/viewer/2022082518/56649ef05503460f94c00488/html5/thumbnails/12.jpg)
Homework
• P. 709
• 2-20 even, 24, 26, 30