Permutations and combinations (with or without repetition)
n is the number of items available, r the number you pick. Combinations ignore order, permutations do not. Results are exact, even very large ones.
Result
10Combinations C(n, r) — order does not matter
- Permutations P(n, r) — order matters
- 60
Inputs
- Number of items n
- 5
- Number picked r
- 3
- Can an item be picked again?
- Without repetition
How it is calculated
Permutations without repetition: P(n, r) = n! ÷ (n − r)!.
Result
Combinations C(n, r) — order does not matter
- Permutations P(n, r) — order matters
- 60
How it is calculated
- Permutations without repetition: P(n, r) = n! ÷ (n − r)!.
- Combinations without repetition: C(n, r) = n! ÷ (r! × (n − r)!).
- With repetition: nʳ permutations and C(n + r − 1, r) combinations.
- Everything is computed with exact integers (BigInt), no rounding.
Example
n = 5, r = 3, without repetition: C(5, 3) = 10 combinations and P(5, 3) = 5 × 4 × 3 = 60 permutations.
Good to know
- n and r are whole numbers from 0 up to 100,000.
- Beyond 400 digits the result is shown as ≈ m × 10ⁿ.
Frequently asked questions
What is this tool used for?
n is the number of items available, r the number you pick. Combinations ignore order, permutations do not. Results are exact, even very large ones.
How is the result calculated?
Permutations without repetition: P(n, r) = n! ÷ (n − r)!.
What should I check before using the result?
n and r are whole numbers from 0 up to 100,000.