Permutations Examples

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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 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.
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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 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.
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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 1st
position, 4 options for the 2nd, 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! 6.41015 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.
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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?

22212019765 22! / (4!)
4.681019 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.
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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 104 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 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.
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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! 2.431018 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.
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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, 15) 20
nPr 15 2.031016