# 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.)

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.

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

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.

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?

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.

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

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.

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

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.

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

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).

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?

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.

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

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.

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

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.

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

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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