Counting principles and tree diagrams
Download
1 / 8

Counting Principles and Tree Diagrams - PowerPoint PPT Presentation


  • 74 Views
  • Uploaded on

Counting Principles and Tree Diagrams. Fundamental counting principle. The Fundamental C ounting Principle states that if there are x ways to choose a first item and y ways to choose a second item, then there are x(y) ways to choose all items. . For example.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Counting Principles and Tree Diagrams' - todd


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

Fundamental counting principle
Fundamental counting principle

  • The Fundamental Counting Principle states that if there are x ways to choose a first item and y ways to choose a second item, then there are x(y) ways to choose all items.


For example
For example

  • A telephone company is assigned a new area code and can issue new 7-digit phone numbers. All phone numbers are equally likely.

  • Find the number of possible 7-digit phone numbers

  • Use the Fundamental Counting Principle:

  • 1st digit 2nd digit 3rd digit 4th digit 5th digit 6th digit 7th digit

  • ? ?? ?? ? ?

  • 10 10101010 10 10

  • There are 10 choices for each digit (0-9), so there are

  • 10(10)(10)(10)(10)(10)(10) = 10,000,000 phone number options


You try
You try

  • A telephone company is assigned a new area code and can issue new 7-digit phone numbers. All phone numbers are equally likely.

  • Find the probability of a phone number that does not contain an 8.

  • First, use the fundamental counting principle to find the number of phone numbers that do not contain an 8.

  • 9(9)(9)(9)(9)(9)(9) = 4,782,969

  • P(no 8) = 4,782,969 = .478

  • 10,000,000


Using a tree diagram
Using a tree diagram

  • The Fundamental Counting Principle tells you only the number of outcomes in some experiments, not what the outcomes are. A tree diagram is a way to show all possible outcomes.

  • For example:

  • A pizza place specializes in two types of crust, sesame and plain, and sells five different toppings, onions, olives, ham, green peppers, and mushrooms. Create a tree diagram to show the options assuming there is only one type of crust with one topping.


Tree diagrams
Tree diagrams

  • Using the Fundamental Counting Principle, we know that we should have 10 options: 2 pizza crusts, 5 toppings…2(5)=10


You try1
You try

  • You are going on a trip. You can pack 2 pairs of pants, 3 shirts, and 2 sweaters for your vacation. Use a tree diagram to show all outfit options you can make if each outfit consists of a pair of pants, a shirt, and a sweater.

  • There are 12 total outfits to choose from

  • 2(3)(2) = 12


The addition counting principle
The addition counting principle

  • If one group contains x objects and a second group contains y objects, and the groups have no objects in common, then there are x + y options.

  • For exampleHow many items can you choose from Bergen’s Deli menu?

  • None of the lists contains identical items, so use the Addition Counting Principle.

  • Total Choices = Sandwiches + Salads + Soups

  • T = 4 + 3 + 3

  • There are 10 total items to choose from