Permutation & Combination Calculator API

About the Permutation & Combination Calculator API

Permutation & Combination Calculator works out nPr and nCr for any total n and selection size r. Send the two integers and get back the number of ordered arrangements, P(n,r), and the number of unordered selections, C(n,r), in one call. It is built for probability calculations, statistics problems, and combinatorial analysis where you need the count rather than a list of the arrangements themselves.

Typical uses include lottery and card-hand odds, the number of possible seating orders or race finishes, how many teams can be drawn from a squad, and checking homework or quiz answers in an education app. Because the result is computed exactly on the server, large inputs do not come back with fractional counts or factorial rounding drift.

The Free plan returns n, r and both results. Paid plans add the formulas used for each calculation, written out in factorial notation, which is useful when the answer is displayed to learners next to the working.

How it works

The calculator takes two non-negative integers, n (the size of the set, up to 170) and r (how many are chosen). r larger than n is rejected with a 400 rather than returning a meaningless count, and so is anything that is not a whole number.

permutation is P(n,r) = n! / (n-r)!, the number of ordered arrangements of r items taken from n. It is computed as the product of the integers from n-r+1 up to n, so the (n-r)! term cancels instead of being built and divided. combination is C(n,r) = n! / (r! (n-r)!), obtained by dividing that product by r!. Both run in exact big-integer arithmetic, which is why C(30,15) returns 155117520 rather than a value a fraction below it.

The results are converted to JSON numbers on the way out. Counts up to 2^53 are exact; larger ones, which appear quickly as n grows, come back as the nearest double, correctly rounded from the exact value, so leading digits and magnitude are right but trailing digits are not. The cap at 170 exists because 171! is larger than a double can hold. Edge cases follow the usual conventions: r = 0 gives 1 for both, and r = n makes the permutation equal to n! and the combination 1.

formulas holds the two expressions as text and is null on the Free plan.

What people use it for

Education

Solve permutation and combination problems for homework and exams

Probability

Calculate odds and probabilities in statistics

Programming

Determine algorithm complexity and counting problems

Game Design

Calculate possible combinations for game mechanics

Ways to call it

One endpoint, many ways in — REST with JSON, XML, YAML and CSV, plus GraphQL and an MCP interface for AI agents.

JSON

Default REST response

XML

Markup format

YAML

Human-readable

CSV

Tabular export

Beta

GraphQL

Query language

New

MCP

For AI agents

Request parameters — GET /v1/permutationcombination

Sent in the query string. Premium parameters are accepted on every plan but only take effect on plans that include them. Anything not listed here is dropped rather than passed through.

Required

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curl "https://api.apiverve.com/v1/permutationcombination?n=10&r=3" \
  -H "x-api-key: YOUR_API_KEY"

Authentication

Send your key in the x-api-key header. That is the only auth step — no token exchange, and no per-endpoint scope to configure.

Response — GET /v1/permutationcombination

Every APIVerve endpoint returns the same three top-level keys, so one response handler covers your whole integration: status, error and data. Only data changes shape.

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{
  "status": "ok",
  "error": null,
  "data": {
    "n": 10,
    "r": 3,
    "permutation": 720,
    "combination": 120,
    "formulas": {
      "permutation": "P(n,r) = n! / (n-r)!",
      "combination": "C(n,r) = n! / (r! × (n-r)!)"
    }
  }
}

Response fields

Paths are relative to data. Premium fields are absent rather than zeroed on plans that do not include them, so check for presence instead of comparing to 0.

Response headers

Every response carries your balance, so your own code always knows where it stands without polling anything. All four are exposed to browsers through CORS.

Errors

Read the HTTP status first, then error for the specific reason. The body names the parameter that has to change.

What a call costs — 1 credits per call

Credits are shared across every APIVerve API — one balance, one key, one bill. Failed requests never count against it, so a rejected input costs nothing.

Calls are what the credits buy at this API's rate — spend them here, on any of the other APIs, or across both. Nothing is reserved per endpoint.

Zero-code embed — one snippet, no backend

Drop an interactive Permutation & Combination Calculator form onto any page. The widget calls the API for you, so no key ever appears in your markup and there is nothing to deploy.

Changelog — Permutation & Combination Calculator API

Every change to this endpoint, newest first. Breaking changes ship as a new version and the previous one keeps serving — response fields are added, never removed or retyped in place, so an integration written against v1 keeps working.

Currently v1