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PERMUTATIONS

This guide explores permutations, focusing on counting arrangements when order matters. We examine various examples, such as how many ways 5 students can be seated at 5 desks and how 7 runners can finish a race. Through detailed explanations, we illustrate permutation notation with 'n' as the total number of objects and 'r' as the number in the arrangement. The guide also considers real-world applications, including committee selections from a group of volunteers, to highlight the importance and utility of permutations in mathematics.

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PERMUTATIONS

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  1. PERMUTATIONS

  2. Permutation Method of counting when order matters Example: Coming in first, second, or third Combination locks

  3. Examples How many ways can 5 students be arranged in 5 desks? There are 5 choices for the first desk, 4 for the second, 3 for the third, etc

  4. Examples How many ways can 5 students be arranged in 5 desks? There are 5 choices for the first desk, 4 for the second, 3 for the third, etc

  5. Examples How many ways can 5 students be arranged in 5 desks? There are 5 choices for the first desk, 4 for the second, 3 for the third, etc

  6. Examples How many ways can 5 students be arranged in 5 desks? There are 5 choices for the first desk, 4 for the second, 3 for the third, etc

  7. Examples How many ways can 5 students be arranged in 5 desks? There are 5 choices for the first desk, 4 for the second, 3 for the third, etc

  8. Examples How many ways can 5 students be arranged in 5 desks? There are 5 choices for the first desk, 4 for the second, 3 for the third, etc

  9. Examples How many ways can 5 students be arranged in 5 desks? There are 5 choices for the first desk, 4 for the second, 3 for the third, etc

  10. Examples How many ways can 5 students be arranged in 5 desks? There are 5 choices for the first desk, 4 for the second, 3 for the third, etc

  11. Examples How many ways can 7 runners finish a race?

  12. Examples How many ways can 7 runners finish a race?

  13. Examples How many ways can 7 runners finish a race?

  14. Permutation Notation n = Number of “objects” to choose from r = Number of “objects” in the arrangement

  15. Simplify

  16. Simplify

  17. Simplify

  18. Simplify

  19. Simplify

  20. Simplify

  21. Simplify

  22. Simplify

  23. Simplify

  24. Example How many permutations are there for the letters H , O , M , E , S

  25. Example How many permutations are there for the letters H , O , M , E , S

  26. Example How many permutations are there for the letters H , O , M , E , S

  27. Example How many permutations are there for the letters H , O , M , E , S

  28. Examples 20 students volunteer to be on a 3-person committee. How many different permutations are there?

  29. Examples 20 students volunteer to be on a 3-person committee. How many different permutations are there?

  30. Examples 20 students volunteer to be on a 3-person committee. How many different permutations are there?

  31. Examples 20 students volunteer to be on a 3-person committee. How many different permutations are there?

  32. ASSIGNMENT 12.6: 1 – 8, 20 – 22, 24, 27 - 29

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