Combinations and Permutations Calculator: API and MCP

Combinations and Permutations Calculator over REST and MCP: input fields, limits, outputs, one example request and its real answer. Free, no sign-up.

Id: math.combinations
Version: 1.0.0
Access: Free
Tool page: Combinations and Permutations Calculator
Schema: GET /api/v1/tools/math.combinations

Input

Field	Type	Constraints	Default	Description
`mode`	string	combination \| permutation \| combinationRepetition \| permutationRepetition	combination	Type of count
`n` (required)	integer	≥ 1, ≤ 1,000		Number of items (n) · How many different items there are to choose from, 1 to 1,000.
`r` (required)	integer	≥ 0, ≤ 1,000		Number chosen (r) · How many items are chosen or arranged, 0 to 1,000.

Output

Field	Type	Description
`result`	string	Number of ways
`digits`	number	Number of digits

Example request

curl -X POST https://hesaplayici.com/api/v1/tools/math.combinations/execute \
  -H 'Content-Type: application/json' \
  -d '{"input":{"mode":"combination","n":10,"r":3},"locale":"en"}'

Example answer

{
  "output": {
    "result": "120",
    "digits": 3
  },
  "steps": [
    {
      "id": "factorial.10",
      "formula": "n! = 1 × 2 × … × n",
      "substitution": "10! = 1 × 2 × … × 10",
      "value": 3628800
    },
    {
      "id": "factorial.3",
      "formula": "r! = 1 × 2 × … × r",
      "substitution": "3! = 1 × 2 × 3",
      "value": 6
    },
    {
      "id": "factorial.7",
      "formula": "(n − r)! = 1 × 2 × … × (n − r)",
      "substitution": "7! = 1 × 2 × … × 7",
      "value": 5040
    },
    {
      "id": "result",
      "formula": "C(n, r) = n! / (r! × (n − r)!)",
      "substitution": "C(10, 3) = 3,628,800 / (6 × 5,040)",
      "value": 120
    }
  ],
  "notes": [],
  "meta": {
    "toolVersion": "1.0.0",
    "locale": "en"
  },
  "citation": {
    "url": "https://hesaplayici.com/en/math/combinations-calculator",
    "title": "Combinations and Permutations Calculator"
  }
}