Permutation & Combination Calculator 🔒 Your data never leaves your browser.
Calculate permutations (nPr) and combinations (nCr) for n items and r chosen.
About this tool
This permutation and combination calculator computes both nPr (permutations) and nCr (combinations) for any n and r you enter, right in your browser, using exact BigInt arithmetic so results stay precise even for large factorials. The key distinction between the two: permutations count arrangements where order matters — think of 1st, 2nd and 3rd place in a race, where swapping two runners' positions creates a different outcome. Combinations count selections where order does not matter — like picking a 3-person committee from a group, where it makes no difference whether you picked Alice before Bob or Bob before Alice; only who ends up on the committee matters.
Because every combination of r items can be arranged in r! different orders, and each of those orderings counts as a separate permutation, permutations are always greater than or equal to combinations for the same n and r (nPr = nCr × r!). Try the default example (n = 10, r = 3): there are 720 ways to arrange 3 of 10 people in a line, but only 120 ways to choose 3 of those same 10 people for a team — the permutation count is exactly 6 times larger, since 3! = 6.
Frequently asked questions
How are permutations and combinations related mathematically?
nPr = nCr × r! — every combination of r items can be arranged in r! (r factorial) different orders, and each of those orderings is counted separately as a distinct permutation. So combinations is always the smaller number: it's permutations with the "which order" information thrown away. For n=10, r=3, that's 720 permutations ÷ 3! (6) = 120 combinations, matching exactly what this calculator shows.