Complete guide
Permutation and combination calculator with repetition
Enter n, r and whether choices may repeat. Calculator24 reports the ordered count, unordered count, exact integers and digit lengths without converting large results to floating point.
Permutation versus combination
A permutation counts arrangements where order matters. A combination counts selections where order does not matter.
Without repetition
Once an item is selected it cannot be selected again. This requires r to be no greater than n.
nPr=n!/(n−r)!nCr=n!/[r!(n−r)!]With repetition
For ordered strings each position can use any of n items. Unordered multisets use the stars-and-bars combination formula.
ordered=n^runordered=C(n+r−1,r)Worked 10 choose 3 example
There are 10×9×8=720 ordered selections. Dividing by 3!=6 removes the internal order and leaves 120 combinations.
Why exact integers matter
Factorials grow quickly. The engine uses BigInt so it does not round large whole-number counts to scientific approximations.
Limits and interpretation
The calculation assumes distinct available items and a fixed repetition rule. Identical objects, adjacency restrictions or conditional choices need specialized counting methods.
Four counting models
| Order | Repetition | Formula |
|---|---|---|
| Matters | No | n!/(n−r)! |
| Does not matter | No | n!/[r!(n−r)!] |
| Matters | Yes | n^r |
| Does not matter | Yes | C(n+r−1,r) |
Frequently asked questions
When should I use a permutation?
When changing the order creates a different outcome.
When should I use a combination?
When only membership matters, not order.
Can r be zero?
Yes. There is one empty selection.
Can r exceed n?
Only when repetition is allowed.
Are large answers exact?
Yes. Counts use integer BigInt arithmetic.
Does the tool list every arrangement?
No. It calculates the number of arrangements.
What to keep in mind
Items are treated as distinct before selection. The calculator returns exact integers up to n and r of 500; it does not enumerate or store the arrangements themselves.
Results display up to 8 decimal places; exported numbers preserve calculation precision. This is a calculation summary, not an official certificate.