Enter n and r to get permutations and combinations, with and without repetition, as exact whole numbers even when they have thousands of digits, plus the formula worked through.
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BigInt arithmetic gives every digit, even for 1000!.
With or without order, with or without repetition.
List all combinations or permutations of your own items.
Use permutations when order matters, such as podium places or PIN codes, and combinations when it does not, such as a lottery draw or a team of three. nPr = n!/(n − r)! and nCr = n!/(r!(n − r)!), so nCr is nPr divided by the r! ways to order each group.
With repetition allowed, each of the r positions can be any of the n items, giving nʳ ordered arrangements. Unordered selections with repetition, like choosing 3 scoops from 5 ice-cream flavours, are counted with the stars and bars formula C(n + r − 1, r).
6 numbers from 49: C(49, 6) = 13,983,816.
4 digits with repetition: 10⁴ = 10,000.
Top 3 of 8 runners: 8P3 = 336.
nPr counts ordered arrangements and nCr counts unordered groups. nCr = nPr / r!.
0! is defined as 1, so there is exactly one way to choose nothing.
You cannot choose more distinct items than you have, so there are no ways to do it.
Up to 10,000. Results are exact; very long numbers are shortened on screen but the Copy button copies every digit.
Up to 12 items. The list shows the first 5,000 arrangements and reports the full count.
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