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Permutations and Combinations

Permutations and Combinations. Objectives. Calculate a permutation. Calculate a combination. Determine whether you should use a combination or permutation to calculate the number of outcomes. . Vocabulary. combination permutation with replacement without replacement . Formulas.

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Permutations and Combinations

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  1. Permutations and Combinations

  2. Objectives • Calculate a permutation. • Calculate a combination. • Determine whether you should use a combination or permutation to calculate the number of outcomes.

  3. Vocabulary • combination • permutation • with replacement • without replacement

  4. Formulas permutation combination without replacement and order is important without replacement and order is NOT important

  5. Find Find

  6. List all the combinations of {a, b, c} when the elements are taken two at a time.

  7. Counting Flow Chart

  8. A group of ten seniors, eight juniors, five sophomores, and five freshmen must select a committee of four. How many committees are possible if there must be one person from each class on the committee?

  9. A group of ten seniors, eight juniors, five sophomores, and five freshmen must select a committee of four. How many committees are possible if there can be any mixture of the classes on the committee?

  10. A group of ten seniors, eight juniors, five sophomores, and five freshmen must select a committee of four. How many committees are possible if there must be exactly two seniors on the committee?

  11. A 7/39 lottery requires choosing seven of the numbers 1 through 39. How many different lottery tickets can you choose? (Order is not important, and numbers do not repeat.)

  12. Which Counting Technique? • What is being selected? • If the selected items can be repeated, use the Fundamental Principle of Counting and multiply the number of choices for each category.

  13. Which Counting Technique? • If there is only one category, use • Combinations if the order of selections does not matter – r is the number of items to be selected from a total of n items • Permutation if the order of selection does matter – r is the number of items to be selected from a total of n items

  14. Which Counting Technique? • If there is more than one category, use the Fundamental Principle of Counting with one box per category. • If you are selecting one item per category, the number in the box for that category is the number of choices for that category. • If you are selecting more than one item per category, the number in the box for that category is found by using step 3.

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