What is the Permutation and Combination Calculator?

It is a tool that computes nPr (permutations) and nCr (combinations) for any n (total items) and r (items chosen), along with n! and r!, so you don't have to work the factorials out by hand.

What is the difference between nPr and nCr?

nPr counts ordered arrangements of r items from n, so ABC and BCA count separately. nCr counts unordered selections, so ABC and BCA count as the same group. nCr is always nPr divided by r!.

How does the calculator compute nCr for large n without overflowing?

Instead of dividing two full factorials, it builds nCr as a running product over the smaller of r and n − r, which stays accurate for far larger n than computing n! directly would allow.

What does the Permutation and Combination Calculator return when r equals 0 or r equals n?

Both are defined edge cases: nCr is 1 when r is 0 or r equals n (there is exactly one way to choose none or all of the items), and nPr is 1 when r is 0.

Can nPr or nCr be negative?

No. If r is greater than n, or either value is negative, the calculator shows an error instead of a nonsensical result — there is no way to arrange or choose more items than are available.

Does the Permutation and Combination Calculator send my n and r values anywhere?

No. The Permutation and Combination Calculator runs entirely in your browser. The values you type are computed locally and never uploaded to ArrayKit.

Permutation and Combination Calculator Online

Calculate nPr and nCr for any n and r in your browser. Your numbers stay on your device.

The Permutation and Combination Calculator runs entirely in your browser. The n and r values you enter are computed locally and are never uploaded to ArrayKit.

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About Permutation and Combination Calculator

Permutation and Combination Calculator finds nPr (permutations) and nCr (combinations) for any n and r, along with n! and r! along the way. Enter the total number of items (n) and how many you are choosing (r), and it instantly shows how many ways you can arrange them in order versus how many ways you can select them regardless of order. It is built for statistics homework, probability problems, lottery and card-hand odds, and any scenario where you need to count arrangements or selections without working the factorials out by hand. A running-product method keeps results accurate for moderate n, well past the point where computing raw factorials would overflow. Built for students, teachers, and anyone who needs a quick nPr or nCr answer. Everything is computed locally in your browser.

Features

Computes nPr (permutations) and nCr (combinations) side by side
Also shows n! and r! for the entered values
Uses a multiplicative method that stays accurate for moderate n
Instant recalculation as you type n and r
Clear error when r is greater than n or a value is not a whole number
Copy the full result summary with one click
Handles the r = 0 and r = n edge cases correctly (both equal 1 for nCr)
Runs entirely in your browser with no numbers sent anywhere

How to use the Permutation and Combination Calculator

Enter n, the total number of items
Enter r, the number of items being chosen
Read nPr for ordered arrangements and nCr for unordered selections
Copy the result summary for your notes or worksheet

Example

Input

n=5, r=2

Output

nPr 20 · nCr 10

Common errors & troubleshooting

The Permutation and Combination Calculator shows an error because r is larger than n. — You can never choose more items than exist. Enter an r between 0 and n, inclusive.
nPr and nCr look swapped compared to what a textbook expects. — nPr counts arrangements where order matters (e.g. race finishes); nCr counts selections where order doesn't (e.g. a committee). Double-check which one your problem needs.
Entering a decimal like 4.5 for n or r produces an error. — Permutations and combinations are only defined for whole numbers. Round or re-enter the value as an integer.
A very large n makes n! or nPr display as ∞. — Factorials overflow double-precision floating point past roughly 170!. nCr for the same n and a small r often still works, since it uses a running product instead of two full factorials.

Frequently asked questions

What is the Permutation and Combination Calculator?: It is a tool that computes nPr (permutations) and nCr (combinations) for any n (total items) and r (items chosen), along with n! and r!, so you don't have to work the factorials out by hand.
What is the difference between nPr and nCr?: nPr counts ordered arrangements of r items from n, so ABC and BCA count separately. nCr counts unordered selections, so ABC and BCA count as the same group. nCr is always nPr divided by r!.
How does the calculator compute nCr for large n without overflowing?: Instead of dividing two full factorials, it builds nCr as a running product over the smaller of r and n − r, which stays accurate for far larger n than computing n! directly would allow.
What does the Permutation and Combination Calculator return when r equals 0 or r equals n?: Both are defined edge cases: nCr is 1 when r is 0 or r equals n (there is exactly one way to choose none or all of the items), and nPr is 1 when r is 0.
Can nPr or nCr be negative?: No. If r is greater than n, or either value is negative, the calculator shows an error instead of a nonsensical result — there is no way to arrange or choose more items than are available.
Does the Permutation and Combination Calculator send my n and r values anywhere?: No. The Permutation and Combination Calculator runs entirely in your browser. The values you type are computed locally and never uploaded to ArrayKit.

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