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Permutation and Combination Calculator

Enter n and r to get the number of permutations and combinations, plus the factorials behind them.

Whole numbers with r no larger than n. Everything is calculated in your browser. Nothing is uploaded.

Results
Permutations5P3
60
Ordered arrangements, where order matters.
Combinations5C3
10
Unordered selections, where order does not matter.
5!
120
n factorial
3!
6
r factorial
(5 - 3)!
2
used to remove order
How it is calculated
Permutations count ordered arrangements.
5P3 = 5! / (5 - 3)! = 60
Combinations divide out the ways to order the chosen items.
5C3 = 5! / (3! × (5 - 3)!) = 10

Everything is calculated in your browser. Nothing is uploaded.

How to calculate permutations and combinations

  1. Enter the total (n)

    Type the total number of items you are choosing from into the n field.

  2. Enter the amount chosen (r)

    Type how many items you are selecting into the r field, keeping r no larger than n.

  3. Read both counts

    The number of permutations and combinations appears instantly, along with the factorials used to reach them.

  4. Copy the results

    Use the copy button to grab every value as a plain-text summary for homework, a report, or a spreadsheet.

Why use this tool

Permutations and combinations together

One entry gives you both nPr and nCr at once, so you never have to guess which one your problem needs or run a second tool.

The factorials are shown, not hidden

Cards for n!, r!, and (n minus r)! reveal exactly how each count is built, which makes the arithmetic easy to check by hand.

Exact big whole numbers

Results are computed as exact integers, so counts like 52 factorial come back in full instead of being rounded off.

Graceful with huge inputs

When a value grows past what can be shown in full, it switches to a readable estimate with its digit count instead of failing.

Runs entirely in your browser

Every count is calculated on your device as you type. Nothing is uploaded, stored, or logged.

About this tool

Permutations and combinations both count how many ways you can choose r items from a set of n, and the only difference is whether order matters. A permutation counts ordered arrangements, so picking first, second, and third place from a race is a permutation. A combination counts unordered selections, so choosing three toppings from a menu is a combination. This calculator takes n and r and reports both counts at once, so you never have to decide which formula to type into a plain calculator and then remember the difference again next time.

Alongside the two headline counts, the tool shows the factorials that produce them: n!, r!, and (n minus r)!. Permutations are n! divided by (n minus r)!, and combinations are that result divided by r!, so seeing every piece makes the arithmetic simple to follow and check. The inputs must be whole numbers with r no larger than n, and the tool explains clearly when a value is out of range rather than showing a broken result. For related math, the scientific calculator handles one-off expressions and the standard deviation calculator summarizes a whole data set.

Counts in combinatorics grow astonishingly fast, so results are computed as exact whole numbers wherever they can be shown in full, and famous figures like the number of ways to shuffle a deck of 52 cards come back complete rather than rounded. When a count grows too large to print as a plain number, the tool shows a compact estimate together with the number of digits, so you still get a useful answer instead of an error. Everything is calculated in your browser as you type and nothing is uploaded.

Frequently asked questions

What is the difference between a permutation and a combination?
A permutation counts arrangements where order matters, so first, second, and third place are all different outcomes. A combination counts selections where order does not matter, so the same three items chosen in any order count once. This tool shows both, so you can pick the one your problem needs.
How are nPr and nCr calculated?
Permutations use nPr = n! divided by (n minus r)!, which counts ordered arrangements. Combinations use nCr = n! divided by r! times (n minus r)!, which removes the duplicate orderings. The calculator shows each factorial so you can trace every step.
What inputs are allowed?
Both n and r must be whole numbers that are zero or greater, and r cannot be larger than n because you cannot choose more items than you have. If you enter a decimal, a negative number, or an r that exceeds n, the tool explains what to fix instead of showing a wrong answer.
What happens when the numbers get very large?
Counts are computed as exact whole numbers whenever they can be shown in full, including large factorials like 52!. If a value grows past what fits as a plain number, it is shown as a compact estimate with its digit count, so you always get a meaningful result rather than an error.
Is my data uploaded anywhere?
No. Every calculation runs in your browser as you type. The numbers you enter are never sent to a server, stored, or logged.

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