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COMBINATIONS

COMBINATIONS. Pencils Down. REVIEW. Basic Fundamental Counting Principle. COUNTING TASK. Non-Similar Objects. Basic Fundamental Counting Principle. COUNTING TASK. Similar Objects. With Restrictions. Basic Fundamental Counting Principle. COUNTING TASK. Similar Objects.

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COMBINATIONS

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  1. COMBINATIONS

  2. Pencils Down

  3. REVIEW

  4. Basic Fundamental Counting Principle COUNTING TASK Non-Similar Objects

  5. Basic Fundamental Counting Principle COUNTING TASK Similar Objects With Restrictions

  6. Basic Fundamental Counting Principle COUNTING TASK Similar Objects Without Restrictions With Replacement

  7. PERMUTATIONS COUNTING TASK Similar Objects Without Restrictions Without Replacement ORDER COUNTS

  8. New Topic Begin Your Notes

  9. Pick from a set of similar elements With No Restrictions With No Replacement Order Does Not Count

  10. COMBINATIONS

  11. How many ways can a committee of three persons be selected from the following group of people? Jane Bob Robin Karen Evan James How many arrangements are there? 6 How many people to select from 3 How many people will be selected

  12. How many ways can a committee of three persons be selected from the following group of people? Jane Bob Robin Karen Evan James

  13. How many ways can a committee of three persons be selected from the following group of people? Jane Bob Robin Karen Evan James Lets look at a committee that contains

  14. Jane Bob Evan

  15. JaneBob Evan Jane Evan Bob BobJane Evan Bob Evan Jane Evan JaneBob EvanBob Jane Are these all the same committee? Yes

  16. JaneBob Evan Jane Evan Bob BobJane Evan Bob Evan Jane Evan JaneBob EvanBob Jane How many duplicates are there? 6

  17. JaneBob Evan Jane Evan Bob BobJane Evan Bob Evan Jane Evan JaneBob EvanBob Jane How could we determine the duplicates without listing them all? Or

  18. JaneBob Evan Jane Evan Bob BobJane Evan Bob Evan Jane Evan JaneBob EvanBob Jane How many ways are there to arrange (in order) three people? Sounds Like A Permutation Problem To Me

  19. JaneBob Evan Jane Evan Bob BobJane Evan Bob Evan Jane Evan JaneBob EvanBob Jane How many ways are there to arrange (in order) three people?

  20. We Had # duplicates

  21. We Had # duplicates

  22. We Had # duplicates

  23. COMBINATION We call this a REPLACE # duplicates With

  24. Divides Out The Duplicates

  25. The General Formula for COMBINATIONS

  26. The General Formula for COMBINATIONS Copy

  27. Our Problem: How many ways can a committee of three persons be selected from the following group of people Jane Bob Robin Karen Evan James Copy

  28. Our Problem: How many ways can a committee of three persons be selected from the following group of people Jane Bob Robin Karen Evan James

  29. Our Problem: How many ways can a committee of three persons be selected from the following group of people Jane Bob Robin Karen Evan James

  30. Our Problem: How many ways can a committee of three persons be selected from the following group of people Jane Bob Robin Karen Evan James

  31. Compute

  32. Compute

  33. Compute

  34. Solution There are 20 ways the committee can be selected

  35. New Problem

  36. New Problem How many ways can a committee of 4 persons be selected from a group of 7 people? Copy

  37. New Problem How many ways can a committee of 4 persons be selected from a group of 7 people? Check for Shortcut OK Similar Objects? Restrictions? Without Replacement?

  38. New Problem How many ways can a committee of 4 persons be selected from a group of 7 people? Does Order Matter?

  39. ? How many ways can a committee of 4 persons be selected from a group of 7 people? ? Formula

  40. How many ways can a committee of 4 persons be selected from a group of 7 people?

  41. Compute

  42. Compute

  43. Solution There are 35 ways the committee can be selected.

  44. Worksheet BB-63

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