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Algebra II

Algebra II. 10.1: Apply the Counting Principle and Permutations HW: p.686-688 (6, 10, 14, 16, 26, 28, 34, 62-68 all) Quiz 10.1-10.3: Friday, 12/13. Fundamental Counting Principle. If one event occurs m ways and another event occurs n ways, then both events occur ways.

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Algebra II

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  1. Algebra II 10.1: Apply the Counting Principle and Permutations HW: p.686-688 (6, 10, 14, 16, 26, 28, 34, 62-68 all) Quiz 10.1-10.3: Friday, 12/13

  2. Fundamental Counting Principle • If one event occurs m ways and another event occurs n ways, then both events occur ways. • (Can be applied for more than two events.)

  3. Application of Fundamental Counting Principle • You have 3 shirts, 4 pairs of pants, and 2 pairs of shoes. How many outfits of 1 shirt, 1 pair of pants, and 1 pair of shoes can you create?

  4. Application of Fundamental Counting Principle • How many different license plates are possible if you have 1 letter followed by 2 digits followed by 3 letters if letters and digits can repeat? • How many plates are possible if letters and digits cannot repeat?

  5. Factorial • What does 9! mean? • Expand and simplify 1.) 2.) 3.) 4.)

  6. Permutations • An ordering of n objects where order is important is a permutation of the objects. • The number of permutations of n objects is n!. • Example: • 10 people are in a race. How many different ways can the people finish in the race?

  7. Permutations • The # of permutations = where n = total # of objects, r = # you are taking. • Example: • 10 people are in a race. How many different ways can 3 people win 1st, 2nd, and 3rd place?

  8. Permutations • You are burning a CD with 13 songs. How many ways can the songs be arranged on the CD?

  9. Permutations • Ms. Wynes’s 2nd period class is playing 7up with a total of 19 students in the class. How many different ways can the people be chosen if order is important?

  10. Permutations with Repetition • The number of permutations of n objects where an object repeats s # of times.

  11. Find the number of distinguishable permutations of the letters in the word. 1.) WYNES 2.) TALLAHASSEE 3.) MATAWAN

  12. Find the number of distinguishable permutations of the letters in the word. 4.) ABERDEEN 5.) CLASSROOM 6.) MATH

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