happytails.ai

Combinations and permutations calculator

Open Combinations and permutations calculator on Happytails.ai. This view has the same page content and links, with explicit tool capabilities. Read the processing notes before using a tool.

Tool capabilities

{
  "id": "combinations-calculator",
  "category": "calculators",
  "built": true,
  "requirements": "Combinations use n! / (r! × (n-r)!). Permutations use n! / (n-r)!. The calculation uses exact integers for n up to 1,000. It does not model selection with replacement.",
  "implementation": {
    "fields": [
      {
        "key": "n",
        "label": "Total items n",
        "value": 52,
        "type": "number",
        "min": 0,
        "max": 1000,
        "step": 1
      },
      {
        "key": "r",
        "label": "Items selected r",
        "value": 5,
        "type": "number",
        "min": 0,
        "max": 1000,
        "step": 1
      },
      {
        "key": "kind",
        "label": "Order",
        "value": "Does not matter (combinations)",
        "type": "select",
        "values": [
          "Does not matter (combinations)",
          "Matters (permutations)"
        ]
      }
    ],
    "input": false,
    "live": true,
    "presentation": "metrics",
    "note": "Choose without replacement from distinct items. Combinations ignore order; permutations count different orders. Uses exact integers for n up to 1,000.",
    "experience": {
      "automatic": true,
      "single": false,
      "inputMaxLength": 1000000,
      "inputMode": "text",
      "label": "Your text",
      "placeholder": "Type or paste your input…",
      "help": "Change the input or settings to update your result. Results update as you type. Up to 1,000,000 characters.",
      "helpParts": [
        "Change the input or settings to update your result.",
        "Results update as you type.",
        "Up to 1,000,000 characters."
      ],
      "action": null
    },
    "mode": "automatic",
    "interactive": false
  },
  "execution": "Browser interface",
  "api": null,
  "browser_agent": {
    "supported": true,
    "name": "run_current_tool",
    "discovery": "WebMCP on the human page in a supporting browser",
    "verification": "See audit/API-AUDIT.md; availability is not verification"
  }
}

Page guide

Count selections, with or without order.

How to use Combinations and permutations calculator
  1. Enter the values you want to calculate and choose the relevant units or settings.
  2. The result updates as you type. Adjust the available settings if needed.
  3. Review the result, then use Copy result or a download link when available.

Useful next steps

List combinationsRandom team generator

How to use it

Enter n distinct items and how many items r you select without replacement. Choose whether a different order should count as another result.

A worked example

Selecting 5 cards from 52 gives 2,598,960 combinations. Choosing an ordered sequence of 3 from 5 items gives 60 permutations.

What to know

Combinations use n! / (r! × (n-r)!). Permutations use n! / (n-r)!. The calculation uses exact integers for n up to 1,000. It does not model selection with replacement.