Permutation and Combination Calculator – nPr & nCr
Count permutations and combinations, with or without repetition.
About the Permutation and Combination Calculator
What is the Permutation and Combination Calculator?
A permutation and combination calculator counts the ways to choose or arrange r items from n, with and without repetition.
Why use this calculator?
Lottery odds, team selection, password counts and scheduling all reduce to these two counting formulas.
How to use it
- Enter n (total items) and r (how many you choose).
- Say whether repetition is allowed.
- Read all four counts: permutations and combinations, with and without repetition.
Formula
nPr = n!/(n−r)!; nCr = nPr/r!; repetition reduces to n^r and C(n+r−1, r).
Values above about 170! are reported as too large for exact display.
Frequently Asked Questions
When do I multiply rather than add?
Count with "and" (arrange A and B) by multiplying; count with "or" (choose A or B) by adding the disjoint cases.
Real lottery odds example?
Picking 6 of 49: C(49,6) ≈ 13.98 million, so your chance is about 1 in 14 million.
What order of operations does this use?
It follows standard PEMDAS/BODMAS rules: parentheses, exponents, multiplication and division, then addition and subtraction.
How precise are the answers?
The calculator uses double-precision floating-point math (about 15 significant digits) and rounds the display. For exact symbolic results use dedicated algebra software.
Can I enter negative numbers or decimals?
Yes. Negative values, decimals and very large or small numbers are all supported unless a field says otherwise.
What does it mean if I get an error?
Errors usually mean an invalid input, such as division by zero or a negative value where only positives make sense. Check your entries and try again.
What is the difference between population and sample?
A population includes every member of a group; a sample is a subset. Sample statistics use n−1 in the denominator to correct for bias.
When should I use median instead of mean?
Use the median when data contains outliers or is skewed, because it is less affected by extreme values than the mean.
What does standard deviation tell me?
It measures how spread out the values are around the mean. A small standard deviation means the data clusters tightly; a large one means it is more scattered.
Is this calculator free to use?
Yes. Every calculator on this site is completely free, with no hidden fees, no subscriptions and no limits on how many times you can use it.