Permutations
Calculator
Results
- Number of permutations
- 95,040
- Number of combinations
- 792
Statistical results
| Number of permutations | 95,040 |
| Number of combinations | 792 |
formula-map diagram
- Number of permutations
- 95,040
- Number of combinations
- 792
Statistical relationship
Formula
P(n, k) = n! / (n − k)!= 95040
Note
This is a simplified model: it applies the displayed standard formula to the summary values you entered and assumes their underlying conditions (independence, normality, correct sampling) hold. It does not analyse a real data set. Check the assumptions before relying on the result.
More in Statistics and probability
See all →Frequently asked questions
What does a permutation calculation give you?+
It gives the number of ways to arrange or order r items selected from a set of n, where the sequence matters. It answers questions like how many different ways you can award gold, silver, and bronze medals among 8 racers.
What is the permutation formula?+
The formula is P(n,r) = n! / (n−r)!, which counts ordered arrangements by taking the total factorial and removing the arrangements of the items not selected. Unlike combinations, there's no division by r! since different orderings count as distinct outcomes.
How much bigger are permutations than combinations for the same n and r?+
Permutations are always r! times larger than the corresponding combination, since for every unordered group there are r! different ways to arrange its members. For 3 items chosen from a set, that's 3! = 6 times more permutations than combinations.
What is P(n,n), the permutation of an entire set?+
P(n,n) equals n!, the factorial of n, since you're arranging every item in the set with none left out. This is why 5 people in a line can be arranged in 5! = 120 different orders.
When should I use permutations instead of combinations?+
Use permutations whenever the arrangement or sequence changes the outcome, such as passwords, race rankings, or seating orders. If swapping two selected items would produce the same practical result, like choosing team members with no distinct roles, you want combinations instead.