MihsabaHow to use
The calculator compares four counting cases from the same n and r: permutations without repetition, combinations without repetition, and the corresponding order-sensitive and order-insensitive counts when repetition is allowed. Results use custom integer arithmetic instead of floating-point numbers so large counts are not rounded.
- Enter n for the total number of distinct items and r for the chosen items or positions.
- Use whole numbers from 0 to 1000 with r ≤ n for the no-repetition cases.
- Calculate to see nPr, nCr and both repetition-allowed counts together.
- Choose the relevant result by asking whether order matters and whether an item may repeat.
How it is calculated
Example
Example n=10, r=3: P(10,3)=720 and C(10,3)=120 without repetition. With repetition allowed, ordered selections are 10³=1000, while unordered selections with repetition are C(12,3)=220.
Important notes
The 1000 limit protects browser responsiveness while keeping the displayed integers exact. nPr and nCr are not evaluated through floating-point factorials. Without repetition r must be ≤ n; the repetition formulas shown are n^r for ordered selections and C(n+r−1,r) for unordered selections.
Frequently asked questions
When should I use permutations instead of combinations?
Use permutations when changing order creates a different outcome; use combinations when only the selected group matters.
Does the calculator support repetition?
Yes. Alongside standard nPr and nCr it shows n^r and C(n+r−1,r) for repetition-allowed cases.
Why not use ordinary floating-point factorials?
Factorials grow very quickly and normal JavaScript numbers lose integer precision, so this tool uses custom exact integer arithmetic.
Is this calculator free?
Yes. It is free to use and requires no account.