Chapter 12: Rational Expressions & Functions

12.8Combinations

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

Finding Combinations

rr

rnrn P

PC

Example 1

37

24

58

C

C

C

Example 2

• Twenty people report for jury duty. How many different twelve-person juries can be chosen?

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.

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?

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?

Rewrite probability as combinations

rt

rf

C

C

total

favorableeventP )(

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?

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?

Homework

• P. 709

• 2-20 even, 24, 26, 30