Permutation & Combination Calculator
nPr and nCr from n and r.
How to use Permutation & Combination Calculator
Compute permutations (nPr) and combinations (nCr) of n items taken r at a time.
Open Permutation & Combination Calculator on toolpermarket and enter your values in the fields below.
In the n (total) field, the total number of items. Must be a non-negative integer.
In the r (choose) field, how many you take at a time. Needs 0 <= r <= n.
Press Calculate to compute the result. The output appears immediately below the form. You can change any input and run it again to compare results.
Read the result and use it as needed. If the number looks off, re-check your inputs and run it again — the math is deterministic, so the same entries always return the same answer.
Worked example. From 8 items choosing 3, there are 336 permutations (order matters) but only 56 combinations (order ignored).
Tips for accurate results.
Permutations count ordered arrangements.
Combinations ignore order, so the number is smaller.
nPr divides by fewer terms than nCr, giving a bigger result.
When to use Permutation & Combination Calculator. Counting possible passwords or line-ups. Sizing lottery-style combinations. Probability and combinatorics problems.
When you actually reach for this
- You want the number of arrangements (nPr) or selections (nCr) from a set.
- You are solving a probability or counting problem.
Where this tool stops being accurate
- Permutations count order; combinations ignore it, so picking the wrong one doubles or halves your answer.
- Large n overflows standard integer range, so results cap out at big values.
Frequently asked questions
When do I use permutation instead of combination?
Use permutation when order matters (a race finish, a lock code). Use combination when order does not (a hand of cards, a committee). Permutations are always at least as large as combinations.
What if r equals n?
Then nPr = n! (every arrangement) and nCr = 1 (there is only one way to take all items when order is ignored).
Why must r not exceed n?
You cannot choose more items than exist. The calculator rejects r > n because such a selection is impossible.
Permutation or combination?
If the order matters (a ranking, a code) use permutation; if it is just a group use combination.
What about repetition?
These count distinct items once; with repeats allowed the formula changes.