Permutations Count
Calculator
Results
- Permutations P(n, r)
- 720
- Combinations C(n, r)
- 120
- Total arrangements (n!)
- 3,628,800
Results
| Permutations P(n, r) | 720 |
| Combinations C(n, r) | 120 |
| Total arrangements (n!) | 3,628,800 |
formula-map diagram
- Permutations P(n, r)
- 720
- Combinations C(n, r)
- 120
- Total arrangements (n!)
- 3,628,800
Formula map
Formula
P(n, r) = n! ÷ (n − r)!= 720
Note
Simplified model: these are exact results of the stated idealised formulas, assuming perfect shapes and exact inputs. Real measurements carry error, and the ellipse perimeter is a Ramanujan approximation. Verify independently before relying on these figures.
More in Mathematics
See all →Frequently asked questions
What do n and r mean in P(n, r)?+
n is the total number of distinct items available, and r is how many of them you are arranging in order. P(n, r) counts the number of ways to pick and order r items from a set of n.
What is the formula?+
P(n, r) = n! / (n-r)!, where ! denotes factorial (the product of all positive integers up to that number). It multiplies n × (n-1) × (n-2) ... down to (n-r+1).
Why does order matter for permutations?+
Permutations count arrangements, so picking items A then B is counted separately from B then A. If order shouldn't matter for your problem, you want combinations instead, not permutations.
What happens if r equals n?+
P(n, n) = n!, since you are arranging all n items in every possible order with none left out — this is simply the total number of ways to order a full set.
What if r is greater than n?+
P(n, r) is undefined (or zero) when r exceeds n, because you cannot arrange more items than you actually have without repeating one, which permutations without repetition do not allow.