9 4 Permutations

9-4 Permutations p 381

Find the number of permutations of a set of objects

Work the hands on mini lab on page 381 with a partner

We want to choose president and vice president from 4 people.

• Demonstrate with volunteers.

• Use the fundamental counting principle to find number of outcomes.

A permutation is an arrangement, or listing, of objects in which order

is important.

• President and vice president vs committee members

Example from mini lab

Factorial (n!)

• 5!=5*4*3*2*1=120

Find each of the following

1. 7!

2. 3!

3. 2!(3!)

Ex) in how many ways can the starting six players of a volleyball team stand in a row for a picture?

• Turn and talk---why is this a permutation?

Ex) The finals of the Middle School Appalachian League features 8

swimmers. In how many ways can the swimmers finish in first of second

place?

• Why is this permutation?

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

• Why is this permutation?

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

In how many ways can you arrange four books on a shelf.

In how many ways can you award 1st and 2nd prize form a group of 6?

In how many ways can 7 people line up at a ticket window?

In how many ways can you arrange the letters in the word eighty?

In how many ways can you choose a leading man and an understudy

from 11 actors?

Coach Malone has an 8-member volleyball team. He told his team that he would start six different

players every game. How many games would it take to do this?

• Why is this not permutation?

The International Club is selling hot dogs at eh Spring Carnival. Customers can select three toppings from among

chili, onions, cheese, mustard, or relish.

• Is this permutation?

What are some key words that help you know it is a permutation?

What are some key words that show it is not a permutation?

Handout—left side onlyLINE CODES

• With a partner

Journal

• How do you find a permutation?

nPrn objects chosen r at a time

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

7P3

p 382: 3-19, 21, 22, 23