Lesson 9-4 Pages 381-383 Permutations Lesson Check 9-3.

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Presentation transcript:

Lesson 9-4 Pages Permutations Lesson Check 9-3

What you will learn! How to find the number of permutations of a set of objects.

PermutationFactorial

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. 32 x = 6 AB AC BA BC CA CB

Example 1: Find the value of the expression. 4 x 3 x 2 x !

Example 2: Find the value of the expression. 3 x 2 x 1 x 5 x 4 x 3 x 2 x ! 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 1 st, 2 nd, and 3 rd 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 1 st place, 6 for 2 nd place, and 5 for 3 rd place. 210 Written as 7 x 6 x 5.

Page 382 Guided Practice #’s 3-6

Pages with someone at home and study examples! Read:

Homework: Page 383 #’s 7-19 all #’s Lesson Check 9-4

How many different three-digit security codes can be made from 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, 1 1, 2 1, 3 1, 4 1, 5 1, 6 2, 1 2, 2 2, 3 2, 4 2, 5 2, 6 3, 1 3, 2 3, 3 3, 4 3, 5 3, 6 4, 1 4, 2 4, 3 4, 4 4, 5 4, 6 5, 1 5, 2 5, 3 5, 4 5, 5 5, 6 6, 1 6, 2 6, 3 6, 4 6, 5 6, 6

1, 1 1, 2 1, 3 1, 4 1, 5 1, 6 2, 1 2, 2 2, 3 2, 4 2, 5 2, 6 3, 1 3, 2 3, 3 3, 4 3, 5 3, 6 4, 1 4, 2 4, 3 4, 4 4, 5 4, 6 5, 1 5, 2 5, 3 5, 4 5, 5 5, 6 6, 1 6, 2 6, 3 6, 4 6, 5 6, 6

1, 1 1, 2 1, 3 1, 4 1, 5 1, 6 2, 1 2, 2 2, 3 2, 4 2, 5 2, 6 3, 1 3, 2 3, 3 3, 4 3, 5 3, 6 4, 1 4, 2 4, 3 4, 4 4, 5 4, 6 5, 1 5, 2 5, 3 5, 4 5, 5 5, 6 6, 1 6, 2 6, 3 6, 4 6, 5 6, 6

1, 1 1, 2 1, 3 1, 4 1, 5 1, 6 2, 1 2, 2 2, 3 2, 4 2, 5 2, 6 3, 1 3, 2 3, 3 3, 4 3, 5 3, 6 4, 1 4, 2 4, 3 4, 4 4, 5 4, 6 5, 1 5, 2 5, 3 5, 4 5, 5 5, 6 6, 1 6, 2 6, 3 6, 4 6, 5 6, 6

1, 1 1, 2 1, 3 1, 4 1, 5 1, 6 2, 1 2, 2 2, 3 2, 4 2, 5 2, 6 3, 1 3, 2 3, 3 3, 4 3, 5 3, 6 4, 1 4, 2 4, 3 4, 4 4, 5 4, 6 5, 1 5, 2 5, 3 5, 4 5, 5 5, 6 6, 1 6, 2 6, 3 6, 4 6, 5 6, 6

1, 1 1, 2 1, 3 1, 4 1, 5 1, 6 2, 1 2, 2 2, 3 2, 4 2, 5 2, 6 3, 1 3, 2 3, 3 3, 4 3, 5 3, 6 4, 1 4, 2 4, 3 4, 4 4, 5 4, 6 5, 1 5, 2 5, 3 5, 4 5, 5 5, 6 6, 1 6, 2 6, 3 6, 4 6, 5 6, 6