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Counting rules

Counting rules. Chapter 4. Lesson 4-1. The Fundamental Counting Principle. Thick. Thin. Pepperoni. Stuffed. Thick. Sausage. Thin. Stuffed. 6. n 1 •. n 2 •. n 3 •…. n k. 2. 3. •. = 6. topping. crust. 5. 2. 3. •. •. = 30. topping. crust. size. 3. 2. 2. •. •.

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Counting rules

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  1. Counting rules Chapter 4

  2. Lesson 4-1 The Fundamental Counting Principle

  3. Thick Thin Pepperoni Stuffed Thick Sausage Thin Stuffed 6

  4. n1 • n2 • n3 •…. nk 2 3 • = 6 topping crust 5 2 3 • • = 30 topping crust size

  5. 3 2 2 • • = 12 eggs side juice

  6. 2 2 2 2 2 • • • • = 32 Q #1 Q#2 Q #3 Q #4 Q#5 1/32

  7. Your turn 4096 1/4096

  8. 6 5 4 3 2 1 • • • • • = 720 8 7 6 5 4 3 2 1 • • • • • • • = 40,320

  9. 8 10 10 10 10 10 10 • • • • • • = 8,000,000

  10. 26 26 26 10 10 10 • • • • • letter letter letter # # # = 17,576,000 (there are about 8,000,000 registered cars in MI) 26 25 24 10 9 8 • • • • • letter letter letter # # # = 11,232,000

  11. Your turn 26 25 24 10 10 10 • • • • • letter letter letter # # # = 15,600,000

  12. Lesson 4-2 Specific Positions

  13. 4 3 2 1 • • • = 24

  14. 1 3 2 1 • • • = 6

  15. 5 4 1 3 2 1 • • • • • = 120 4 1 1 3 2 1 • • • • • = 24 3 2 1 3 2 • • • • • 1 = 36

  16. 3 4 3 2 1 2 • • • • • = 144 5 4 3 2 1 4 = 480 • • • • • 3 3 2 2 1 1 = 36 • • • • •

  17. Your turn…examples 4 – 7 7 6 5 4 3 2 1 • • • • • • 7! = 5040 4 5 4 3 2 1 3 • • • • • • = 1440

  18. 7 7 7 7 • • • = 2401 7 6 5 4 = 840 • • •

  19. 5 8 8 8 = 2560 • • • 5 7 6 5 = 1050 • • •

  20. Lesson 4-3 Permutations and Combinations

  21. 9 9 9 = 729 • • n • n • n • n…. = nr r times

  22. 7 6 5 4 3 2 1 • • • • • • = 5040 n!

  23. 7 6 5 4 • • • = 840 = 7P4

  24. 20! 20P3 = 6840 = 17!

  25. 6 J C Yes J A C J C A Permutation A J A C

  26. 3 J C No J A C J C A Combination A J A C

  27. 5! 5P3 = 60 = 2! 60

  28. 60 = 10 10 6

  29. 3! 3! 3C2 = 3 3P2 = 6 = = 1! 2! 1!

  30. 20! 20P4 = 116,280 = 16! 20! 20C4 = 4845 = 16! 4!

  31. 8C2 = 28 5P5 = 120

  32. 14C4 = 1001 9C3 = 84 = 12P5 = 95040

  33. Lesson 4-4 Permutations and Combinations for Multiple Groups

  34. 4P4 = 24 2-letter: 4P2 = 12 Total = 60 3-letter: 4P3 = 24 4-letter: 4P4 = 24

  35. 6P4 = 360 1-digit: 6P1 = 6 2-digit: 6P2 = 30 Total = 516 3-digit: 6P3 = 120 4-digit: 6P4 = 360

  36. 4-digit: 6P4 = 360 5-digit: 6P5 = 720 Total = 1800 6-digit: 6P6 = 720

  37. Your turn Total = 246 5 people: 9C5 = 126 6 people: 9C6 = 84 7 people: 9C7 = 36

  38. 15C6 = 5005 9C4 = 126

  39. 11C4 = 330 29C20 = 10,015,005 27C7 = 888,030 9C7 = 36

  40. Lesson 4-5

  41. 6! = 720 R E MM S U 6! = 360 2! R E MM S U

  42. AAA N N B A AANN B AAA N N B A AANN B AAA N N B AAA N N B 6! = 60 AAA N N B 3! 2! AAA N N B

  43. n! p! n! q! p! n! q! p! r! 11! = 34650 4! 4! 2!

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