N Choose R Permutation Formula

The permutation formula describes the possible permutations of r elements out of a group of n elements where order does matter.

Calculate Four Choose Three Order Matters

To calculate four choose three where order matters, you can use the formula for n choose r permutations. For example if we want to calculate the possible permutations of choosing three items from the set {♥︎,♦︎,♣︎,♠︎} we can set up the formula:

First we substitute four in for the variable to represent the size of the set. Then we substitute three for the variable to represent the number of items we are choosing.

To double check our work, we can display the twenty four unique permutations of these three items. Note, if order did not matter, you can use the formula for combinations.

  1. { ♦︎, ♥︎, ♠︎ }
  2. { ♦︎, ♠︎, ♥︎ }
  3. { ♥︎, ♦︎, ♠︎ }
  4. { ♥︎, ♠︎, ♦︎ }
  5. { ♠︎, ♥︎, ♦︎ }
  6. { ♠︎, ♦︎, ♥︎ }
  7. { ♣︎, ♥︎, ♠︎ }
  8. { ♣︎, ♠︎, ♥︎ }
  9. { ♥︎, ♣︎, ♠︎ }
  10. { ♥︎, ♠︎, ♣︎ }
  11. { ♠︎, ♥︎, ♣︎ }
  12. { ♠︎, ♣︎, ♥︎ }
  13. { ♦︎, ♣︎, ♠︎ }
  14. { ♦︎, ♠︎, ♣︎ }
  15. { ♣︎, ♦︎, ♠︎ }
  16. { ♣︎, ♠︎, ♦︎ }
  17. { ♠︎, ♣︎, ♦︎ }
  18. { ♠︎, ♦︎, ♣︎ }
  19. { ♦︎, ♥︎, ♣︎ }
  20. { ♦︎, ♣︎, ♥︎ }
  21. { ♥︎, ♦︎, ♣︎ }
  22. { ♥︎, ♣︎, ♦︎ }
  23. { ♣︎, ♥︎, ♦︎ }
  24. { ♣︎, ♦︎, ♥︎ }

Calculate Four Choose Two Order Matters

To calculate four choose two where order matters, you can use the formula for n choose r permutations. For example if we want to calculate the possible permutations of choosing twp items from the set {♥︎,♦︎,♣︎,♠︎} we can set up the formula:

First we substitute four in for the variable , representing the size of the set. Then we substitute two for the variable , representing the number of items we are choosing.

To double check our work, we can display the twelve possible permutations of these two items chosen from the set. Note, if order did not matter, you can use the formula for combinations.

  1. { ♥︎, ♠︎ }
  2. { ♠︎, ♥︎ }
  3. { ♦︎, ♠︎ }
  4. { ♠︎, ♦︎ }
  5. { ♥︎, ♦︎ }
  6. { ♦︎, ♥︎ }
  7. { ♣︎, ♠︎ }
  8. { ♠︎, ♣︎ }
  9. { ♥︎, ♣︎ }
  10. { ♣︎, ♥︎ }
  11. { ♣︎, ♦︎ }
  12. { ♦︎, ♣︎ }