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12.1 The Fundamental Counting Principle and Permutations

12.1 The Fundamental Counting Principle and Permutations. Objective: SWBAT Use the fundamental counting principle and permutations. F.C.P. If one event can occur in ways and another can occur in ways, then the number of ways that both events can occur is ways.

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12.1 The Fundamental Counting Principle and Permutations

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  1. 12.1 The Fundamental Counting Principle and Permutations Objective: SWBAT Use the fundamental counting principle and permutations

  2. F.C.P. • If one event can occur in ways and another can occur in ways, then the number of ways that both events can occur is ways. • This is not limited to only 2 events. • Example: Suppose you want to make a sandwich and have the choices of: ham, turkey, roast beef, or pastrami for meats; wheat, white, or rye for beads; and mayonnaise, mustard, or relish for spreads.

  3. Tree Diagram 36 Different Choices!! Or

  4. ! • Factorial is ! • Example: • …always! • Questions?!

  5. Permutations • Orders an object in a set amount of ways. Order matters for permutations. • Example: There are 8 movies that I will see in theaters this summer. How many different ways can I see the movies?

  6. Permutations continued • Consider this problem: There are 12 songs that you want to download from iTunes but you can only get 4 due to your funds running out. How many different ways could you get 4 of these 12 songs? • Mathematicians developed this to help:

  7. Permutations with repetition • How many ways can the letters in the word MISSISSIPPI be written? • Where n is the number of letters and the q’s are where one object repeats q times.

  8. Assignment • Read section 12.1 • Pg. 705 #6-50e, 68-80e

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