Math-MCP

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permutations

Calculate the number of ordered permutations (nPr) for given total items and selected count. Returns exact decimal value.

Instructions

Calculates ordered selections nPr exactly; returns a decimal string

Tool call template

Replace each placeholder with a value matching the input schema. Only required parameters are included; add optional parameters as needed.

{
  "id": 1,
  "jsonrpc": "2.0",
  "method": "tools/call",
  "params": {
    "arguments": {
      "total": "<total>",
      "selected": "<selected>"
    },
    "name": "permutations"
  }
}

Input Schema

Name	Required	Description	Default
`total`	Yes	Total number of items, n
`selected`	Yes	Number of ordered selections, r

Schema Changelog

Changes observed during successful MCP inspections.

First observedv0.3.0Jul 28, 2026

TDQS

A3.7/5.0

Behavior3/5

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

No annotations provided, so description carries full burden. It states exact calculation and decimal string output but does not disclose potential large number handling or constraints like r ≤ n.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness5/5

Is the description appropriately sized, front-loaded, and free of redundancy?

Single sentence, front-loaded with action verb, no wasted words. Highly concise and efficient.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness3/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

Sufficient for a simple math tool with two parameters and no output schema, but misses mention of constraints (e.g., r ≤ n) and edge cases.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters3/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema already describes both parameters (total, selected) with 100% coverage. Description adds no new parameter-level information, remaining at baseline.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose5/5

Does the description clearly state what the tool does and how it differs from similar tools?

Description uses specific verb 'Calculates' and resource 'ordered selections nPr exactly; returns a decimal string'. Clearly differentiates from sibling 'combinations' by specifying 'ordered'.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines3/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

Implies usage through 'ordered selections' but no explicit when-to-use or when-not-to-use compared to sibling tools like 'combinations'. Lacks alternatives guidance.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.