Number of Permutations for N Distinct Items

To calculate the possible permutations of n distinct items, you can take the factorial of n to get the numer of permutations. For example if we want to calculate the possible permutations of this unique set of items {♥︎,♦︎,♣︎,♠︎} we can set up the formula:

Then we substitute four in for the variable , representing the size of the set.

To double check our work, we can display the twenty four unique permutations of these four items.

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

Links

Permutation | formula