# 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. { ♠︎, ♣︎, ♦︎, ♥︎ }