Unit 5 Notes ­ Day 2 ­ Permutations and Combinations.notebook November 06, 2013

Permutations

Permutation: an arrangement of objects in a specific order.

2 Important Traits of Permutations:

1. Order Matters

2. No Repetitions

Example: How many ways can you arrange 3 people for a picture?

Factorial:

Factorial can be found on the graphing calculator.

Steps:

1. enter the number (n)

2. Math

3. Prb

4. 4:!

5. enter

Example: Suppose a business owner has a choice of 5 locations in which to establish her business. She decides to rank them from best to least according to certain criteria. How many different ways can she rank them?

Example. What if in the previous problem, she wanted to rank only the top 3?

Permutation Rule:

n = total # of objects r = how many you need

"n objects taken r at a time"

Unit 5 Notes ­ Day 2 ­ Permutations and Combinations.notebook November 06, 2013

Example: Remember the business woman who wanted to rank the top 3 out of 5? This is a permuation.

Permutations can be found on the graphing calculator.

Example: Find

Steps:

1. 5

2. Math

3. Prb

4. 2:nPr

5. 3

6. enter

Example: A TV news director wishes to use 3 news stories on the evening news. She wants the top 3 news stories out of 8 possible. How many ways can the program be set up?

Example: How many ways can a chairperson and an assistant be selected for a project if there are 7 scientists available?

Example: How many different ways can I arrange 3 box cars selected from 8 to make a train?

Example: How many ways can 4 books be arranged on a shelf if they can be selected from 9 books?

Unit 5 Notes ­ Day 2 ­ Permutations and Combinations.notebook November 06, 2013

A factorial is also a permutation.

Look at the previous example.

How many ways can 4 books be arranged on a shelf if they can be selected from 9 books?

Note:

Order Words:

How many ways can I

listen

sing

read

1st, 2nd, etc

pres/vice pres

chair/assistant

eat

Special Permutation when letters MUST repeat . . .

Example: How many permutations of the word seem can be made?

This leads to another permutation rule when some things repeat:

It reads: the # of permutations of n objects in which k1 are alike, k2 are alike, etc.

Example: Find the permutations of the word Mississippi.

Unit 5 Notes ­ Day 2 ­ Permutations and Combinations.notebook November 06, 2013

Combinations

Combination: a selection of "n" objects WITHOUT regard to order.

Order does NOT matter.

Example: Let's compare ABCD - Find permutations of 2 and combinations of 2.

When different orderings of the same items are counted separately, we have a permutation problem, but when different orderings of the same items are not counted separately, we have a combination problem.

Combination Rule:

Read: "n" objects taken "r" at a time.

Example: How many combinations of 4 objects are there, taken 2 at a time?

There is a key on the graphing calculator:

Find

Steps:

1. 4

2. Math

3. Prb

4. 3: nCr

5. 2

6. enter

Unit 5 Notes ­ Day 2 ­ Permutations and Combinations.notebook November 06, 2013

Example: To survey opinions of customers at local malls, a researcher decides to select 5 from 12. How many ways can this be done. (Hint: Order is not important.)

Example: A bike shop owner has 11 mountain bikes in the showroom. He wishes to select 5 to display at a show. How many ways can a group of 5 be selected? (Hint: He is NOT interested in a specific order.)

Example: In a club there are 7 women AND 5 men. A committee of 3 women AND 2 men is to be chosen. How many different possibilities are there? (HINT: The AND indicates that you must use the multiplication rule along with the combination rule.)

Example: In a club with 7 women and 5 men, select a committee of 5 with AT LEAST 3 women. (HINT: You must use the multiplication rule as well as the addition rule.)

Example: In a club with 7 women and 5 men, select a committee of 5 with AT MOST 2 women. (HINT: You must use the multiplication rule and the addition rule.)