Download presentation

Presentation is loading. Please wait.

Published byEmory Boyd Modified over 2 years ago

1
Warm-Up Problem Can you predict which offers more choices for license plates? Choice A: a plate with three different letters of the alphabet in any order Choice B: a plate with four different nonzero digits in any order. By the end of class, you should be able to successfully answer this question.

2
Example 1 Eight pieces of paper are numbered from 1 to 8 and placed in a box. One piece of paper is drawn from the box, its number is written down, and the piece of paper is replaced in the box. A second piece of paper is drawn from the box, and its number is written down. If the two numbers are added together, how many different ways can a total of 12 be obtained?

3
Example 2 Eight pieces of paper are numbered from 1 to 8 and placed in a box. One piece of paper is drawn from the box and its number is written down. A second piece of paper is drawn from the box, and its number is written down. If the two numbers are added together, how many different ways can a total of 12 be obtained?

4
Example 3 You have three books that you want to place on a shelf. How many different ways can you arrange the books on the shelf?

5
The Counting Principle Let E 1 and E 2 be two events. The first event E 1 can occur m different ways. The second event E 2 can occur n different ways. The number of ways that the two events can occur is m times n.

6
Example 3 again. You have three books that you want to place on a shelf. How many different ways can you arrange the books on the shelf? 6 different ways to place 3 books on a shelf.

7
Example 4 You have five books and you want to place three of them on a shelf. How many different ways can you arrange three of the five books on the shelf? 60 different ways

8
This is the number of different arrangements or permutations of 5 things taken 3 at a time. This can be written as P(5,3). Remember: Permutations of n Elements taken r at a time is found by Key Words: arrangements, schedule, order

9
Example 5 Eight horses are running in a race. In how many different ways can these horses come in first, second, and third? Assume there are no ties. Using the Counting Principle: 8(7)(6)=336. Using Permutations:

10
Example 6 Your teacher gives you a list of three books. You must choose two of the books on the list to read. How many different pairings can you choose from?

11
Combinations When you choose r elements from a large set of n elements and ORDER DOES NOT MATTER, You are finding the number of combinations of n elements taken r at a time. Key Words: group, committee, selection, sample

12
Example 7 How many different committees of 3 people can be chosen from a group of 8 people? Since order does not matter, use combinations 56 committees

13
Warm-Up Problem Can you predict which offers more choices for license plates? Choice A: a plate with three different letters of the alphabet in any order Choice B: a plate with four different nonzero digits in any order. Alphabet – 15,600 Numbers - 3024

Similar presentations

OK

Sullivan Algebra and Trigonometry: Section 14.2 Objectives of this Section Solve Counting Problems Using the Multiplication Principle Solve Counting Problems.

Sullivan Algebra and Trigonometry: Section 14.2 Objectives of this Section Solve Counting Problems Using the Multiplication Principle Solve Counting Problems.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on wifi technology free download Ppt on power system stability using facts devices Ppt on measuring central venous pressure Animated ppt on magnetism projects Ppt on recycling of waste oil Ppt on satellite orbit Ppt on suspension type insulators home Ppt on types of forest found in india Ppt on horizontal axis windmill Ppt on different occupations in india