Lesson 9-4 Pages 381-383

Permutations

Lesson Check 9-3

What you will learn!

How to find the number of permutations of a set of

objects.

PermutationPermutation

FactorialFactorial

What you really need to know!

The expression n factorial (n!) is the product of all counting numbers beginning with n and counting backward to 1.

6! = 6 x 5 x 4 x 3 x 2 x 1 = 720

What you really need to know!

A permutation is an arrangement, or listing, of objects in which order is important. You can use the Fundamental Counting Principle to find the number of possible arrangements.

Link to Pre-Made Lesson

Example of a Permutation:

You must pick 2 letters from the letters A, B, C to form a two letter code for computer access. Each letter can only be used once. How many codes can be made.

3 2x = 6A BA CB AB CC AC B

Example 1:

Find the value of the expression.

4 x 3 x 2 x 124

4!

Example 2:

Find the value of the expression.

3 x 2 x 1 x 5 x 4 x 3 x 2 x 1

720

3! • 5!

Example 3:

A team of bowlers has five members who bowl one at a time. In how many orders can they bowl?

Example 3:

This is a permutation. There are 5 choices for the first bowler, 4 for the second, 3 for the third, 2 for the fourth, and 1 for the fifth.

120

Written as 5!

Example 4:

A school fair holds a raffle with 1st, 2nd, and 3rd place prizes. Seven people enter the raffle. How many ways can the three prizes be awarded?

Example 3:

This is part of a permutation. There are 7 choices for 1st place, 6 for 2nd place, and 5 for 3rd place.

210

Written as 7 x 6 x 5.

Page 382

Guided Practice

#’s 3-6

Pages 381-382 with someone at home and study

examples!

Read:

Homework: Page 383

#’s 7-19 all

#’s 21-24

Lesson Check 9-4

How many different three-digit security codes can be madefrom the digits 1, 2, 3, 4, and 5 if no digit is repeated in a code?

Page

585

Lesson 9-4

Lesson Check 9-4

Prepare for Mid-Test!

Page

384

#’s 1-16

1, 11, 1 1, 21, 2 1, 31, 3 1, 41, 4 1, 51, 5 1, 61, 6

2, 12, 1 2, 22, 2 2, 32, 3 2, 42, 4 2, 52, 5 2, 62, 6

3, 13, 1 3, 23, 2 3, 33, 3 3, 43, 4 3, 53, 5 3, 63, 6

4, 14, 1 4, 24, 2 4, 34, 3 4, 44, 4 4, 54, 5 4, 64, 6

5, 15, 1 5, 25, 2 5, 35, 3 5, 45, 4 5, 55, 5 5, 65, 6

6, 16, 1 6, 26, 2 6, 36, 3 6, 46, 4 6, 56, 5 6, 66, 6

1, 11, 1 1, 21, 2 1, 31, 3 1, 41, 4 1, 51, 5 1, 61, 6

2, 12, 1 2, 22, 2 2, 32, 3 2, 42, 4 2, 52, 5 2, 62, 6

3, 13, 1 3, 23, 2 3, 33, 3 3, 43, 4 3, 53, 5 3, 63, 6

4, 14, 1 4, 24, 2 4, 34, 3 4, 44, 4 4, 54, 5 4, 64, 6

5, 15, 1 5, 25, 2 5, 35, 3 5, 45, 4 5, 55, 5 5, 65, 6

6, 16, 1 6, 26, 2 6, 36, 3 6, 46, 4 6, 56, 5 6, 66, 6

1, 11, 1 1, 21, 2 1, 31, 3 1, 41, 4 1, 51, 5 1, 61, 6

2, 12, 1 2, 22, 2 2, 32, 3 2, 42, 4 2, 52, 5 2, 62, 6

3, 13, 1 3, 23, 2 3, 33, 3 3, 43, 4 3, 53, 5 3, 63, 6

4, 14, 1 4, 24, 2 4, 34, 3 4, 44, 4 4, 54, 5 4, 64, 6

5, 15, 1 5, 25, 2 5, 35, 3 5, 45, 4 5, 55, 5 5, 65, 6

6, 16, 1 6, 26, 2 6, 36, 3 6, 46, 4 6, 56, 5 6, 66, 6

1, 11, 1 1, 21, 2 1, 31, 3 1, 41, 4 1, 51, 5 1, 61, 6

2, 12, 1 2, 22, 2 2, 32, 3 2, 42, 4 2, 52, 5 2, 62, 6

3, 13, 1 3, 23, 2 3, 33, 3 3, 43, 4 3, 53, 5 3, 63, 6

4, 14, 1 4, 24, 2 4, 34, 3 4, 44, 4 4, 54, 5 4, 64, 6

5, 15, 1 5, 25, 2 5, 35, 3 5, 45, 4 5, 55, 5 5, 65, 6

6, 16, 1 6, 26, 2 6, 36, 3 6, 46, 4 6, 56, 5 6, 66, 6

1, 11, 1 1, 21, 2 1, 31, 3 1, 41, 4 1, 51, 5 1, 61, 6

2, 12, 1 2, 22, 2 2, 32, 3 2, 42, 4 2, 52, 5 2, 62, 6

3, 13, 1 3, 23, 2 3, 33, 3 3, 43, 4 3, 53, 5 3, 63, 6

4, 14, 1 4, 24, 2 4, 34, 3 4, 44, 4 4, 54, 5 4, 64, 6

5, 15, 1 5, 25, 2 5, 35, 3 5, 45, 4 5, 55, 5 5, 65, 6

6, 16, 1 6, 26, 2 6, 36, 3 6, 46, 4 6, 56, 5 6, 66, 6

1, 11, 1 1, 21, 2 1, 31, 3 1, 41, 4 1, 51, 5 1, 61, 6

2, 12, 1 2, 22, 2 2, 32, 3 2, 42, 4 2, 52, 5 2, 62, 6

3, 13, 1 3, 23, 2 3, 33, 3 3, 43, 4 3, 53, 5 3, 63, 6

4, 14, 1 4, 24, 2 4, 34, 3 4, 44, 4 4, 54, 5 4, 64, 6

5, 15, 1 5, 25, 2 5, 35, 3 5, 45, 4 5, 55, 5 5, 65, 6

6, 16, 1 6, 26, 2 6, 36, 3 6, 46, 4 6, 56, 5 6, 66, 6