# Combinations and permutations calculator

- Human page: https://happytails.ai/en/calculators/combinations-calculator/
- Markdown: https://happytails.ai/en/calculators/combinations-calculator.md
- Structured JSON: https://happytails.ai/agents/en/calculators/combinations-calculator/index.json
- Visibility: public

## Tool capabilities

| Property | Value |
| --- | --- |
| Tool ID | `combinations-calculator` |
| Category | calculators |
| Implementation | Registered implementation. Registration alone is not a production-quality guarantee. |
| Browser execution | Automatic updates after valid input or file selection. |
| Browser processing | Browser; see tool notes for network behavior. |
| HTTP API | Not callable through HTTP. |
| Browser-agent interface | run_current_tool |

### Implementation notes

Choose without replacement from distinct items. Combinations ignore order; permutations count different orders. Uses exact integers for n up to 1,000.

### Inputs and settings

No free-text input is required. Use the file inputs and/or settings below.

| Setting | Meaning | Control type | Default | Constraints |
| --- | --- | --- | --- | --- |
| `n` | Total items n | number | 52 | min=0 max=1000 step=1 |
| `r` | Items selected r | number | 5 | min=0 max=1000 step=1 |
| `kind` | Order | select | "Does not matter (combinations)" | Allowed: Does not matter (combinations), Matters (permutations) |

### Browser-agent workflow

1. Open the human page in a browser that supports WebMCP.
2. Discover the interface exposed by that page; use its actual schema.
3. Select files on the page first when the tool requires files.
4. Call `run_current_tool` with valid input and settings.
5. Inspect the returned result or error and the displayed output. Retrieve files from the displayed download links.

Calls do not automatically copy or download results. Browser permissions still apply. Interface availability alone is not proof of successful execution.

### Planning specification

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.

This describes intended requirements. Use the implementation notes, interface schema and observed output to determine current support.

### Complete machine-readable capability record

```json
{
  "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.",
      "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 can we improve this tool?

Report a problem or share an idea.

Please leave out private information. Your message and the tool name go to our team via PostHog.

### 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 combinations](https://happytails.ai/en/text-tools/list-combinations/) ([Markdown](https://happytails.ai/en/text-tools/list-combinations.md))

- [Random team generator](https://happytails.ai/en/education-tools/random-team-generator/) ([Markdown](https://happytails.ai/en/education-tools/random-team-generator.md))

## 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.