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Permutations Examples

Permutations Examples. 1. How many different starting rotations could you make with 6 volleyball players? (Positioning matters in a rotation.). Permutations Examples. 6 •5•4•3•2•1 = 6! = 720

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Permutations Examples

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  1. Permutations Examples 1. How many different starting rotations could you make with 6 volleyball players? (Positioning matters in a rotation.)

  2. Permutations Examples 6•5•4•3•2•1 = 6! = 720 There are 6 options for the 1st position, then 5 options remaining for the 2nd position, 4 for the 3rd position, etc., until there is only 1 option left for the last position. 1. How many different starting rotations could you make with 6 volleyball players? (Positioning matters in a rotation.)

  3. Permutations Examples 2. How many different starting lineups could you make with 11 soccer players, if each player could play any position?

  4. Permutations Examples 11! = 39,916,800 There are 11 options for the 1st position, then 10 options remaining for the 2nd position, 9 for the 3rd position, etc., until there is only 1 option left for the last position. 2. How many different starting lineups could you make with 11 soccer players, if each player could play any position?

  5. Permutations Examples 3. How many different starting lineups could you make with 11 soccer players, if only 1 player can play goalie, 5 players can play any of 5 forward positions, and 5 players can play any of 5 defense/midfield positions?

  6. Permutations Examples 3. How many different starting lineups could you make with 11 soccer players, if only 1 player can play goalie, 5 players can play any of 5 forward positions, and 5 players can play any of 5 defense/midfield positions? 1•5!•5! = 14,400 Only 1 player can play goalie. For the forwards, there are 5 options for the 1st position, 4 options for the 2nd, etc. It works the same for the 5 defenders.

  7. Permutations Examples 4. How many seating charts could a teacher make with 18 students in a class, and 18 available desks?

  8. Permutations Examples 18! = 6.4•1015 There are 18 options for the 1st seat, then 17 options remaining for the 2nd seat, 16 for the 3rd seat, etc., until there is only 1 option left for the last seat. 4. How many seating charts could a teacher make with 18 students in a class, and 18 available desks?

  9. Permutations Examples 5. How many seating charts could a teacher make with 18 students in a class, and 22 available desks?

  10. Permutations Examples 22•21•20•19•…•7•6•5 = 22! / (4!) = 4.68•1019 There are 22 seats to choose from for the 1st student, then 21 seats remaining for the 2nd student, 20 for the 3rd student, etc., until there are 5 seats left to choose from for the last student. 5. How many seating charts could a teacher make with 18 students in a class, and 22 available desks?

  11. Permutations Examples 6. How many codes are possible for a lock that has 4 digits, and each digit can be a number 0-9?

  12. Permutations Examples 10•10•10•10 = 104 = 10,000 You can repeat numbers, so each digit has 10 possibilities (0-9). 6. How many codes are possible for a lock that has 4 digits, and each digit can be a number 0-9?

  13. Permutations Examples 7. How many codes are possible for a lock that has 4 digits, and each digit can be a number 0-9 or a letter A-F?

  14. Permutations Examples 16•16•16•16 = 164 = 65,536 The numbers 0-9 and the letters A-F form the hexadecimal system, which is frequently used with computers. As the name suggests there are 16 possibilities for each digit. 7. How many codes are possible for a lock that has 4 digits, and each digit can be a number 0-9 or a letter A-F?

  15. Permutations Examples 8. In how many ways can you arrange 20 books on a bookshelf, if they are in a single row?

  16. Permutations Examples 20! = 2.43•1018 There are 20 books to choose from for the 1st position, then 19 books remaining for the 2nd position, 18 for the 3rd position, etc., until there is only 1 book left for the last position. 8. In how many ways can you arrange 20 books on a bookshelf, if they are in a single row?

  17. Permutations Examples 9. In how many ways can you rank your favorite 3 movies from a list of 10?

  18. Permutations Examples 10•9•8 = 720 The key word here is rank, indicating that order matters. Ranking A-B-C as your first three choices is different from ranking C-B-A as your first three choices. Because order matters, you do not need any division. 9. In how many ways can you rank your favorite 3 movies from a list of 10?

  19. Permutations Examples 10. In how many ways can you rank your favorite 5 books from a list of 20?

  20. Permutations Examples 20•19•18•17•16 = 20! / (15!) = P(20, 5) = 20 nPr 5 =1,860,480 10. In how many ways can you rank your favorite 5 books from a list of 20?

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