1 / 17

Permutations: Finding the Number of Arrangements

Learn how to calculate the number of permutations for a set of objects using factorial expressions. Practice solving permutation problems with step-by-step examples.

carlestrada
Download Presentation

Permutations: Finding the Number of Arrangements

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. Transparency 4 Click the mouse button or press the Space Bar to display the answers.

  2. Splash Screen

  3. Example 4-4b Objective Find the number of permutations of a set of objects

  4. Example 4-4b Vocabulary Permutation An arrangement, or listing, of objects in which order is important

  5. Example 4-4b Vocabulary Factorial The expression n! is the product of all counting numbers beginning with n and counting backwards to 1 4! = 4  3  2  1 24

  6. Example 4-4b Math Symbols ! Factorial

  7. Lesson 4 Contents Example 1Evaluate Factorials Example 2Evaluate Factorials Example 3Find a Permutation Example 4Find a Permutation

  8. Find the value of Example 4-1a Write problem Write out definition of 4! Multiply using factorial key on calculator Answer: 24 1/4

  9. Find the value of Example 4-1b Answer: 120 1/4

  10. Find the value of the expression Example 4-2a Write problem Write the definition of 3! Write the definition of 5! 6  120 Multiply using the calculator Answer: 2/4

  11. Find the value of the expression Example 4-2b Answer: 144 2/4

  12. Example 4-3a BOWLINGA team of bowlers has five members who bowl one at a time. In how many orders can they bowl? 5! This is an example of a permutation 5  4  3  2  1 Write the permutation Write the definition of the permutation 120 orders Answer: Multiply 3/4

  13. Example 4-3b TRACK AND FIELDA relay team has four members who run one at a time. In how many orders can they run? Answer: 24 orders 3/4

  14. Example 4-4a RAFFLEA 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? 7 choices for 1st prize 6 choices for 2nd prize 5 choices for 3rd prize This is a modified type of permutation 7 6 5 Since the person with 1st place cannot compete for 2nd place, there only 6 people for 2nd prize The people that won 1st and 2nd prizes cannot compete for 3rd prize 4/4

  15. Example 4-4a RAFFLEA 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? 7 choices for 1st prize 6 choices for 2nd prize 5 choices for 3rd prize 7 6 5 7  6  5 Multiply the numbers 210 ways Answer: 4/4

  16. Example 4-4b * SAILINGNine boats are competing in a sailing race. How many ways can medals for 1st, 2nd, and 3rd place be awarded? Answer: 504 ways 4/4

  17. End of Lesson 4 Assignment

More Related