1 / 21

Fundamental Counting Principle

Fundamental Counting Principle. Today. Review Independent and Dependent Events Review Factorials (from 8 th Grade Math) Learn what the Counting Principle says Complete Examples to grasp the concept of the Fundamental Counting Principle JEOPARDY GAME Short Worksheet for homework.

travis
Download Presentation

Fundamental Counting Principle

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. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Fundamental Counting Principle

  2. Today Review Independent and Dependent Events Review Factorials (from 8th Grade Math) Learn what the Counting Principle says Complete Examples to grasp the concept of the Fundamental Counting Principle JEOPARDY GAME Short Worksheet for homework

  3. Dependent Events • If the outcome of one event affects the outcome of another, then the events are said to be Dependent Events. • Example • Taking out a marble from a bag containing some marbles and not replacing it, and then taking out a second marble are dependent events.

  4. Independent Events • Independent events are events where the outcome of one event does not affect the outcome of the other events. • Example • Tossing a coin and rolling a number cube are independent events.

  5. Dependent/Independent Events Review Which of the following are dependent events? (write down A, B, C, D) Getting an even number in the first roll of a number cube and getting an even number in the second roll. Getting an odd number on the number cube and spinning blue color on the spinner. Getting a face card in the first draw from a deck of playing cards and getting a face card in the second draw. (The first card is not replaced.) A. 1 B. 2 and 3 C.3 D. 1 and 3

  6. Factorials • Factorial denoted as n!, with n > 0, is an expression, which is the product of all positive integers starting with n and counting backward to 1. For example, 4! = 4 . 3 . 2 . 1 and n! = n . n-1 .  n-2 . . . . 3. 2. 1 • Example • Find the factorial of 8. • 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 40,320

  7. Why do we need the Fundamental Counting Principle? You are going to a movie. The theater sells 3 sizes of popcorn (small, medium, and large) with 3 choices of toppings (no butter, butter, extra butter).  How many different ways can you purchase bag of popcorn?

  8. Is anyone having trouble with this problem?Whether you are or not, here is how we make problems like that one easier.

  9. Fundamental Counting Principle The total number of options for a succession of choices is the product of the number of options for the individual choices.

  10. Why is the FCP important? The FCP is the guiding rule for finding the number of ways to accomplish two or more tasks. It is also the fastest way of counting how many options you have.

  11. Demonstration

  12. Independent/Dependent Events It does not matter whether you are dealing with Independent Events or Dependent Events, the FCP will work for both and in the same way.

  13. Example 1 • Information about girls' ice skates:Colors:  white, beige, pink, yellow, blueSizes: 4, 5, 6, 7, 8Extras:  tassels, striped laces, bellsAssuming that all skates are sold with ONE extra, how many possible arrangements exist? • Questions • How many events are occurring? • How many options are there for each event? • Is the event Independent or Dependent?

  14. Answer to Example 1 • How many events are occurring? 3 • Colors, Sizes, Extras • How many options are there for each event? • Colors = 5 • Sizes = 5 • Extras = 3 • Independent or Dependent? • All of these events are independent • So, the total number of outcomes is 5 x 5 x 3 = 75

  15. Example 2 • Your state issues license plates consisting of letters and numbers.  There are 26 letters and the letters may be repeated.  There are 10 digits and the digits may be repeated.  How many possible license plates can be issued with two letters followed by three numbers? • Questions • How many events are occurring? • Is the event Independent or Dependent? • How many options are there for each event?

  16. Answer to Example 2 • How many events are occurring? 5 • 5 different placeholders on the license plate • How many options are there for each event? • 1st placeholder is a letter so there are 26 options • 2nd placeholder is a letter so there are 26 options • 3rd placeholder is a number so there are 10 options • 4th placeholder is a number so there are 10 options • 5th placeholder is a number so there are 10 options • Independent or Dependent? • All are Independent So, the total number of outcomes is 26 x 26 x 10 x 10 x 10 = 676,000

  17. Example 3 • The ice cream shop offers 31 flavors.  You order a double-scoop cone.  In how many different ways can the clerk put the ice cream on the cone if you wanted two different flavors? • Questions • How many events are occurring? • Is the event Independent or Dependent? • How many options are there for each event?

  18. Answer to Example 3 • How many events are occurring? 2 • There are two scoops of Ice Cream • How many options are there for each event? • Scoop 1 = 31 • Scoop 2 = 30 • Independent or Dependent? • These events are dependent because you want two different flavors • So, the total number of outcomes is 31 x 30 = 930

  19. Can you see? The Fundamental Counting Principle is a way of showing you all the options you have in your life. You may not realize it now, but almost every choice you make has options to it, and sometimes, you will get a different result when alternate options are chosen.

  20. Jeopardy Game!

  21. Review Today’s Lesson FCP - The total number of options for a succession of choices is the product of the number of options for the individual choices. Knowing this will come in handy in the next few lesson! Worksheet is due tomorrow!

More Related