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Counting Principle, Permutation & Combination

Counting Principle, Permutation & Combination. Dwayne Strachan Edtech 597 Multiple Principle Lesson Weeks 15-16. The wardrobe of a clown. How many different costumes can I make?. I have three clown shirts I have two clown pants I have four clown shoes. 1. 2. 3. 4. 7. 8. 5. 6. 9.

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Counting Principle, Permutation & Combination

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  1. Counting Principle, Permutation & Combination Dwayne Strachan Edtech 597 Multiple Principle Lesson Weeks 15-16

  2. The wardrobe of a clown

  3. How many different costumes can I make? • I have three clown shirts • I have two clown pants • I have four clown shoes

  4. 1 2 3 4

  5. 7 8 5 6

  6. 9 11 12 10

  7. 13 15 16 14

  8. 19 20 17 18

  9. 21 23 24 22

  10. The Counting Principle notation The number of outcomes of an event is the product of the number of outcomes in each stage of the event. m = the number of outcomes in the first stage n = the number of outcomes in the second stage

  11. The Counting Principle 3 x 2 x 4 24

  12. The Counting Principle • Let’s say you were out for dinner and had a choice of three appetizers, five entrees and 4 desserts. • How many different dinners could you create. • Go to the next page for the solution.

  13. Counting Principle 3 5 4 x x = 60 different dinners

  14. Permutation • I have six pictures I want to hang on the wall • How many different permutations can I arrange them in?

  15. Permutation A B C A C B B C A B A C C A B C B A

  16. Permutation 6 x 5 x 4 x 3 x 2 x 1 720 arrangements

  17. The Permutation Notation n = the number of items that can be used r = the number of items that will be used

  18. Permutation = 720 different arrangements 0! = 1

  19. Permutation • What do you think you would do if all pictures were not included in the arrangement? • Find the number of three picture arrangements that can be made from the six original pictures. • Go to the next page for the solution.

  20. 6 x 5 x 4 = 120 different arrangements

  21. Combination A B C A C B B C A B A C C A B C B A

  22. Combination Sue Pat Ben Gus Sue & Ben Sue & Gus Sue & Pat Pat & Ben Pat & Gus Pat & Sue Ben & Sue Ben & Pat Ben & Gus Gus & Sue Gus & Pat Gus & Ben

  23. The Combination Notation n = the number of items that can be used r = the number of items that will be used

  24. Combinations • How many different three letter nonsense words can be made from the word MATH? • Go to the next page for the answer.

  25. Combination = 10 words

  26. Counting Principle, Permutation and Combination • The counting principle will find the number of outcomes in an event. • A permutation is a unique arrangement of elements selected from a group of elements. • A combination is a group of objects selected from a group of elements without consideration of order.

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