1 / 13

Understanding Counting Methods and Permutations in Rational Expressions

This chapter explores counting methods and permutations, crucial for combinatorial problems. Through engaging examples, we illustrate how to calculate the number of possible outfits from a given selection of clothing items using tree diagrams and the multiplication counting principle. We also delve into routes between cities, the arrangement of athletes in races, and possibilities for pizza toppings, all employing counting techniques. Finally, we provide exercises to practice these concepts, aiding in understanding rational expressions and functions.

zamir
Télécharger la présentation

Understanding Counting Methods and Permutations in Rational Expressions

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. Chapter 12: Rational Expressions & Functions 12.7 Counting Methods & Permutations

  2. Example 1 • Suppose you have three shirts and two pair of pants that coordinate well. Make a tree diagram to find the number of possible outfits you have.

  3. Example 1a • Suppose you have two shirts and four pairs of shorts you could bring for gym class. What is the most possible outfits you have for gym?

  4. Multiplication Counting Principle • If there are m ways to make a first selection, and n ways to make a second selection, there are m x n ways to make the two selections. • Example: • For five shirts and eight pairs of shorts, the number of possible outfits is 5 x 8 = 40

  5. Example 2 • On the map there are two tunnels for cars going from NJ to Manhattan, NY, and three bridges from Manhattan to Brooklyn, NY. How many routes using a tunnel and then a bridge are there from NJ to Brooklyn through Manhattan?

  6. Example 2a • At the neighborhood pizza shop, there are five vegetable toppings and three meat toppings for a pizza. How many different pizzas can you order with one meat and one vegetable topping?

  7. Permutations • Arrangement of objects in a specific order • Written as:

  8. Example 3 • How many different batting orders can you have with 9 baseball players?

  9. Example 3a • A swimming pool has eight lanes. In how many ways can eight swimmers be assigned lanes for a race?

  10. Example 4 • Simplify:

  11. Example 5 • Suppose you use six different letters to make a computer password. Find the number of possible six-letter passwords.

  12. Example 5a • Suppose your cousin needs to choose a four-digit number to use with a new debit card. Find the number of possible four-digit numbers without repeating a digit.

  13. Homework • P. 702 • 2-24 even, 30, 34

More Related