Permutation & Combination for AI Agents

Overview

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

Live Test Permutation & Combination for AI Agents Source →

The tool

Once your client is connected to the VerveContext server, this appears in its tool list as PermutationCombinationforAIAgents. It is read-only and open-world — it fetches and never mutates anything on your side — so most clients call it without asking you to confirm.

Tool call

{
  "name": "PermutationCombinationforAIAgents",
  "arguments": {
    "n": "10",
    "r": "3"
  }
}

You do not name the tool yourself; the model picks it. Asking about 10 in the terms this source covers is enough for it to reach for PermutationCombinationforAIAgents on its own — naming it explicitly also works, and is the way to force the call.

Connecting

One server URL covers every source in the catalog, including this one. Authorization is OAuth: the client opens a browser once, and there is no key to paste into a config file.

{
  "mcpServers": {
    "vervecontext": {
      "url": "https://api.vervecontext.com/v1/mcp"
    }
  }
}

Per-client setup — Claude, Cursor, VS Code, ChatGPT — is on the MCP setup page.

Arguments

These are the properties on the tool's inputSchema, so a well-behaved client validates them before the call is made. Premium arguments are accepted on every plan but only take effect on plans that include them.

Argument	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

What the model gets back

The result carries a structuredContent object matching the tool's declared outputSchema, so a client reads fields without parsing prose. status is "ok" and error is null on success; a null field means the value was not available for that input, not that the call failed.

Result

{
  "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
`formulas.permutation`Premium	string	`P(n,r) = n! / (n-r)!`	Mathematical formula used for permutation calculation
`formulas.combination`Premium	string	`C(n,r) = n! / (r! × (n-r)!)`	Mathematical formula used for combination calculation

Why ground on it

A model can produce something that looks like this answer from its training data, and be confidently out of date or simply wrong. This source returns the current value in a shape you can check, which is the difference between an answer you can cite and one you have to hedge.

Point an evaluation at permutation: it is the field most worth pinning a claim to, and it is either present and current or absent — never plausibly invented.

Failure modes

Errors come back as tool errors carrying a sentence the model can act on, not a bare status code. Error handling covers the full list.

Status	What it means
`400` / `422`	The arguments did not validate. The message names the offending one.
`401`	The OAuth session is invalid or expired — reconnect the server.
`403`	Blocked by a key restriction or an IP allow-list. Never a bad identity.
`404`	This source is not part of VerveContext. Check the catalog.
`429`	Out of credits, or a brief rate limit. The message tells them apart.

A call costs 2 credits each time the tool actually runs; a model that reasons about the tool without calling it costs nothing.

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 for AI Agents

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

Call it as a REST APIOne HTTPS endpoint and an x-api-key header, with SDKs for Node, Python and .NET.APIVerve →Reference →

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

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