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Aim #10-7: How do we use the permutation formula?

Aim #10-7: How do we use the permutation formula?. A permutation is an ordered arrangement of items that occurs when: No item is used more than once. The order of the arrangement makes a difference. Example 1: Using the Formula for Permutations. Check for Understanding:.

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Aim #10-7: How do we use the permutation formula?

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  1. Aim #10-7: How do we use the permutation formula? • A permutation is an ordered arrangement of items that occurs when: • No item is used more than once. • The order of the arrangement makes a difference.

  2. Example 1: Using the Formula for Permutations

  3. Check for Understanding:

  4. Example 2: Using the Formula • You need to arrange seven of your favorite books along a small shelf . In how many different ways can you arrange the books, assuming that the order of the books makes a difference to you?

  5. Check for Understanding: • In how many ways can six books be lined up along a shelf?

  6. How do we distinguish between combinations and permutations? • A combination occurs when: • The items are selected from the same group. • No item is used more than once. • The order of the items makes no difference. Note: • Permutations problems involve situations which order matters.

  7. Example 3:

  8. Solution:

  9. Check for Understanding: • For each of the following problems explain if the problem is one involving permutations or combinations. • How many ways can you select 6 free DVD’s from a list of 200 DVDs? • In a race in which there are 50 runners and no ties, in how many ways can the first three finishers come in?

  10. A Formula for Combinations

  11. Example 4: • A three-person committee is needed to study ways of improving public transportation. How many committees could be formed from the eight people on the board of supervisors?

  12. Check for Understanding: • From a group pf 10 physicians, how many ways can four people be selected to attend a conference on acupuncture?

  13. Example 8:

  14. Check for Understanding: • How many different 4-card hands can be dealt from a deck that has 16 different cards?

  15. Summary: Answer in complete sentences. Explain what is a permutation. How do permutations and combinations differ? How do you solve each?

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