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Chapter 10

Chapter 10. Counting Techniques. Miscellaneous Counting Methods Section 10.4. Permutations and Combinations . Three cards are dealt in succession and without replacement from a standard deck of 52 cards . In how many different orders can the cards be dealt ?

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Chapter 10

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  1. Chapter 10 Counting Techniques

  2. Miscellaneous Counting MethodsSection 10.4

  3. Permutations and Combinations • Three cards are dealt in succession and without • replacement from a standard deck of 52 cards. • In how many different orders can the • cards be dealt? • How many different 3-card hands are possible? 52 nPr 3 = 52 x 51 x 50 = 132,600 52 x 51 x 50 3 x 2 x 1 52 nCr 3 = = 22,100

  4. Permutations and Combinations The playbook for the quarterback of the Dallas Cowboys contains 50 plays. In how many different ways could the quarterback select 3 plays to use in succession in the next three downs? In how many different ways could he select a set of 3 plays to study? 50 x 50 x 50 = 125,000 50 x 49 x 48 3 x 2 x 1 50 nCr 3 = = 19,600

  5. Permutations and Combinations Peter must select three electives from a group of 7 courses. • In how many ways can Peter do this? • If all 7 courses are available each of the 4 hours from 8 AM to noon, from how many • different schedules (hours and what course • at each hour) can Peter choose? 7 x 6 x 5 3 x 2 x 1 7 nPr 4 = 7 x 6 x 5 x 4= 840 7 nCr 3 = = 35

  6. Distinct Arrangements • The total number of distinctarrangements of n objects, where p objects are identical, q objects are identical, r objects are identical, and so on, is given by

  7. Distinct Arrangements How many different arrangements can be made with the letters in the word TALLAHASSEE? How many different arrangements can be made with the letters in the word MISSISSIPPI? 11! 3!2!2!2! 39,916,800 48 39,916,800 6x2x2x2 = 831,600 = = 39,916,800 1152 39,916,800 24x24x2 11! 4!4!2! = 34,650 = = END

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