🔀 Permutation & Combination Calculator

About this Permutation & Combination Calculator

Permutations count arrangements where order matters (podium finishes, passwords); combinations count selections where it doesn't (committees, lottery picks). Enter n (the total items) and r (how many are chosen or arranged) and get both nPr and nCr instantly — computed with overflow-safe multiplication, with scientific notation for results too big to write out.

How to use it

1. Enter n, the total number of items.
2. Enter r, how many are chosen or arranged.
3. Click Calculate nPr & nCr.
4. Use nPr when order matters and nCr when it doesn't.

Example

From 10 players, podium finishes for gold, silver and bronze: 10P3 = 720; choosing any 3 for a team: 10C3 = 120.

Frequently asked questions

Why is nPr always bigger than nCr?

Every unordered group of r items can be arranged in r! different orders, so nPr = nCr × r!. Order multiplies the possibilities.

How are lottery odds calculated?

As a combination: a 6-from-49 lottery has 49C6 = 13,983,816 possible tickets — which is why jackpots are so hard to win.

More Calculators