{
  "id": "permutation-and-combination-calculator",
  "version": "1.0.0",
  "name": "Permutation and Combination Calculator",
  "shortName": "Permutation & combination",
  "description": "Calculate exact permutations and combinations with or without replacement.",
  "category": "Math & Statistics",
  "categorySlug": "math-statistics",
  "keywords": [
    "permutation and combination",
    "permutation",
    "combination",
    "npr",
    "ncr",
    "combinatorics",
    "with replacement"
  ],
  "status": "live",
  "workStatus": "pending",
  "reviewStatus": "pending",
  "migrationStatus": "new",
  "engine": "native",
  "creator": null,
  "reviewer": null,
  "quality": {
    "availability": "live",
    "technicalReviewRecord": "/reviews/permutation-and-combination-calculator.json",
    "qualifiedReview": "pending",
    "qualifiedReviewer": null,
    "qualifiedReviewDate": null,
    "formulaVersion": "1.0.0",
    "referenceCoverage": "references-listed",
    "releaseTestScope": "Catalog and regression checks are not a professional formula audit; consult release evidence.",
    "historicalMetadataDate": "2026-08-25",
    "historicalMetadataNotice": "The imported date is not evidence of a completed human review."
  },
  "urls": {
    "page": "/calculator/permutation-and-combination-calculator/",
    "definition": "/calculator/permutation-and-combination-calculator/definition.json",
    "schema": "/calculator/permutation-and-combination-calculator/schema.json",
    "llms": "/calculator/permutation-and-combination-calculator/llms.txt",
    "legacyDefinition": "/calculator/permutation-and-combination-calculator.json"
  },
  "queryExample": "https://askcalculators.com/calculator/permutation-and-combination-calculator/?totalItems=6&selectedItems=2&replacement=without",
  "queryParameters": {
    "totalItems": {
      "label": "Total amount in the set (n)",
      "type": "number",
      "required": true,
      "default": 6
    },
    "selectedItems": {
      "label": "Amount in each subset (r)",
      "type": "number",
      "required": true,
      "default": 2
    },
    "replacement": {
      "label": "Selection rule",
      "type": "select",
      "required": true,
      "default": "without"
    }
  },
  "inputs": [
    {
      "id": "totalItems",
      "label": "Total amount in the set (n)",
      "type": "number",
      "required": true,
      "defaultValue": 6,
      "min": 0,
      "max": 500,
      "step": 1,
      "width": "half"
    },
    {
      "id": "selectedItems",
      "label": "Amount in each subset (r)",
      "type": "number",
      "required": true,
      "defaultValue": 2,
      "min": 0,
      "max": 500,
      "step": 1,
      "width": "half"
    },
    {
      "id": "replacement",
      "label": "Selection rule",
      "type": "select",
      "required": true,
      "defaultValue": "without",
      "options": [
        {
          "label": "Without replacement",
          "value": "without"
        },
        {
          "label": "With replacement",
          "value": "with"
        }
      ],
      "width": "full"
    }
  ],
  "outputs": [
    {
      "id": "permutations",
      "label": "Permutations",
      "format": "text",
      "primary": true
    },
    {
      "id": "combinations",
      "label": "Combinations",
      "format": "text"
    },
    {
      "id": "permutationFormula",
      "label": "Permutation formula",
      "format": "text"
    },
    {
      "id": "combinationFormula",
      "label": "Combination formula",
      "format": "text"
    }
  ],
  "formula": {
    "expression": "Without replacement: nPᵣ=n!/(n−r)! and nCᵣ=n!/[r!(n−r)!]; with replacement: nʳ and C(n+r−1,r)."
  },
  "examples": [
    {
      "label": "Reproducible default-input example (not a personal recommendation)",
      "inputs": {
        "totalItems": 6,
        "selectedItems": 2,
        "replacement": "without"
      }
    }
  ],
  "sources": [
    {
      "label": "Calculator.net reference calculator",
      "url": "https://www.calculator.net/permutation-and-combination-calculator.html"
    }
  ]
}