Maths Probability
Permutation calculator
Items available (n)
Positions to fill (r)
Permutations (nPr) 720
P(10,3) = n! ÷ (n−r)!
Combinations (nCr) 120
With repetition allowed 1,000
All n arranged (n!) 3,628,800
Combinations with repetition 220
Order matters · repetition changes everything
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320 × 100
A permutation counts ordered arrangements: P(10,3) = 720 ways to award gold, silver and bronze among ten runners. Allowing repetition gives 10³ = 1,000 instead, which is the right count for a three-digit code.
How to count permutations
1 Enter how many items are available and how many positions to fill.
2 Read nPr for ordered selection without repetition.
3 Use the repetition row when an item can be reused.
4 Compare against combinations to see the r! factor.
The repetition distinction is what separates a podium from a padlock. Three medals among ten runners is 720 — nobody wins twice. A three-wheel padlock with ten digits is 1,000, because each wheel is independent. The padlock is larger despite the same n and r, which is why combination locks are named misleadingly: they are permutation locks, and order very much matters.
Questions
n! divided by (n−r)! — the number of ordered arrangements of r items from n.
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300 × 250
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