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Permutation Investigations

Permutation Investigations. Honors Analysis. Ft. Thomas Exchange. Section 1.1 VocabularY. Independent Events : Events that do not affect each other Sample Space : List of all possible outcomes

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Permutation Investigations

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  1. Permutation Investigations Honors Analysis

  2. Ft. Thomas Exchange

  3. Section 1.1 VocabularY • Independent Events: Events that do not affect each other • Sample Space: List of all possible outcomes • Fundamental Counting Principle: If events are independent, the number of ways both can occur is the product of the number possible outcomes for each event. • Permutation: An arrangement in which ORDER MATTERS

  4. Permutations • In how many unique orders can 5 people sit in a row of chairs? • In how many orders can the letters of the word “pencil” be arranged? • In how many ways can five people place first, second, and third in a race?

  5. Permutation Investigations 5P3 is a notation for writing the permutation of 5 items taken 3 at a time. 5P3 6P4 = 8P2= How might you calculate these values using only factorials?? Use your pattern to write a formula for the permutation of n items taken r at a time: nPr

  6. Permutations with Repetition • The goal: Find the number of possible arrangements in the word MISSISSIPPI

  7. Permutations with Repetition • Calculate the following factorial values: 0! = 1! = 2! = 3! = 4! = 5! = 6! = 7! =

  8. Permutations with Repetition Determine the number of unique arrangements created by the following sets of letters and complete the chart: Do you notice any patterns? **Hint: Factorials!

  9. Permutations with Repetition • How many arrangements could be created from the letters in “cheese” if only the e’s can be moved and are distinct from each other (try using e1 e2 e3) CH____S__ How might this help you develop a formula?

  10. Circular Permutations • In how many orders can you sit 3 people around a table? (Careful – no “beginning point”) • 4 people? • 5 people? • Do you notice a pattern?

  11. Additional Counting Methods The chart below shows information about Math Club members: In how many ways could a boy OR girl be selected? In how many ways could a sophomore OR a girl be selected? If order matters, in how many ways could two boys be selected? (A boy AND a boy)

  12. Vocabulary • Events are mutually exclusive if one excludes the other from happening. n(A or B) = n(A) + n(B) • If events are non-mutually exclusive, be careful to subtract the number of ways the events can overlap! n(A or B) = n(A) + n(B) – n(A ∩ B) • Multiple Dependent Events: n(A and B) = n(A) · n(B | A), where n(B | A) is the number of ways event B can occur after A occurs

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