Permutation & Combination Calculator API Reference

Overview

Perfect for probability calculations, statistics problems, and combinatorial analysis in mathematics.

Endpoint

One host, one path per API. The block below shows this call in four languages; every one of them is the same HTTP request. Making requests covers the timeouts, retries and parameter rules that apply to all of them. The SDKs wrap the same call in a typed client.

GEThttps://api.apiverve.com/v1/permutationcombination

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

const res = await fetch('https://api.apiverve.com/v1/permutationcombination?n=10&r=3', {
  headers: { 'x-api-key': 'your_api_key_here' },
});

if (!res.ok) throw new Error(`${res.status} ${await res.text()}`);

const { data } = await res.json();
console.log(data);

import requests

res = requests.get(
    "https://api.apiverve.com/v1/permutationcombination?n=10&r=3",
    headers={"x-api-key": "your_api_key_here"},
    timeout=15,
)
res.raise_for_status()

print(res.json()["data"])

package main

import (
	"fmt"
	"io"
	"net/http"
)

func main() {
	req, _ := http.NewRequest("GET", "https://api.apiverve.com/v1/permutationcombination?n=10&r=3", nil)
	req.Header.Set("x-api-key", "your_api_key_here")

	res, err := http.DefaultClient.Do(req)
	if err != nil {
		panic(err)
	}
	defer res.Body.Close()

	out, _ := io.ReadAll(res.Body)
	fmt.Println(string(out))
}

Replace your_api_key_here with the key from your dashboard. When the inputs arrive as a list rather than one at a time, batch requests run up to 200 of them through this same API in a single call.

Authentication

Send your key in the x-api-key header. That is the only auth step — there is no token exchange and no per-endpoint scope to configure. Authentication covers creating, rotating and revoking keys.

401 is the only auth verdict

A 401 means the key is missing, invalid or expired. A 403 means the key is valid but not permitted here — blocked by a key restriction or an IP allow-list. Running out of credits is a 429.

Parameters

Sent in the query string. Premium parameters are accepted on every plan but only take effect on plans that include them.

Parameter	Type	Description
`n`Required	integer	Total number of items range 0–170
`r`Required	integer	Number of items to choose (must be <= n) range 0–170

Response

Every API returns the same three top-level keys, so one response handler covers your whole integration: status, error and data. Only data changes shape. Response format covers the envelope, the other output formats and how premium fields are withheld.

Sample response

{
  "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.

Field	Type	Example	Description
`n`	number	`10`	Total number of items used in calculation
`r`	number	`3`	Number of items chosen in calculation
`permutation`	number	`720`	Calculated permutation P(n,r) result value
`combination`	number	`120`	Calculated combination C(n,r) result value
`formulas`Premium	object	`{...}`	Object containing mathematical formulas for permutation and combination
`permutation`Premium	string	`"P(n,r) = n! / (n-r)!"`	Mathematical formula used for permutation calculation
`combination`Premium	string	`"C(n,r) = n! / (r! × (n-r)!)"`	Mathematical formula used for combination calculation

Errors

Read the HTTP status first, then error for the specific reason. The body names the parameter that has to change. Error handling covers the full status list and which of them are worth retrying.

Status	Meaning	What to do
`400`	Input was rejected	Read `error`; it names the parameter.
`401`	Key missing or invalid	Check the header name and the key value.
`403`	Key valid, but not permitted	A key restriction or IP allow-list; see key scoping.
`429`	Rate limited, or out of credits	Read `error` to tell them apart; see rate limits.

Use cases

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

Other ways to use Permutation & Combination Calculator

Set up Permutation & Combination Calculator on APIVerve, or reach the same source a different way. Your APIVerve account and credits work on all of them — one key, one balance.

Give it to an AI agentConnect over MCP and your agent calls it as a native tool — Claude, Cursor, ChatGPT.VerveKit →Reference →

Use it in Google Sheets or ExcelA =VERVE() formula fills a column — no script, no export, recalculates in place.VerveSheets →Reference →

Ground an agent on itA cited, machine-checkable fact your model can't produce on its own.VerveContext →Reference →

Permutation & Combination Calculator