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

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Permutations Examples 1. How many different starting rotations could you make with 6 volleyball players? (Positioning matters in a rotation.) 654321 = 6! = 720 There are 6 options for the 1 st position, then 5 options remaining for the 2 nd position, 4 for the 3 rd position, etc., until there is only 1 option left for the last position.

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

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

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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?

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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? 15!5! = 14,400 Only 1 player can play goalie. For the forwards, there are 5 options for the 1 st position, 4 options for the 2 nd, etc. It works the same for the 5 defenders.

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

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Permutations Examples 4. How many seating charts could a teacher make with 18 students in a class, and 18 available desks? 18! = 6.410 15 There are 18 options for the 1 st seat, then 17 options remaining for the 2 nd seat, 16 for the 3 rd seat, etc., until there is only 1 option left for the last seat.

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

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Permutations Examples 5. How many seating charts could a teacher make with 18 students in a class, and 22 available desks? 22212019…765 = 22! / (4!) = 4.6810 19 There are 22 seats to choose from for the 1 st student, then 21 seats remaining for the 2 nd student, 20 for the 3 rd student, etc., until there are 5 seats left to choose from for the last student.

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

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Permutations Examples 6. How many codes are possible for a lock that has 4 digits, and each digit can be a number 0-9? 10101010 = 10 4 = 10,000 You can repeat numbers, so each digit has 10 possibilities (0-9).

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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?

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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? 16161616 = 16 4 = 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.

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

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Permutations Examples 8. In how many ways can you arrange 20 books on a bookshelf, if they are in a single row? 20! = 2.4310 18 There are 20 books to choose from for the 1 st position, then 19 books remaining for the 2 nd position, 18 for the 3 rd position, etc., until there is only 1 book left for the last position.

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

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Permutations Examples 9. In how many ways can you rank your favorite 3 movies from a list of 10? 1098 = 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.

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

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Permutations Examples 10. In how many ways can you rank your favorite 5 books from a list of 20? 2019181716 = 20! / (15!) = P(20, 5) = 20 nPr 5 =1,860,480

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