Compute nCr and nPr for a set size and selection. Pure CPU, instant.
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": {
"n": "<n>"
},
"name": "combinations"
}
}| Name | Required | Description | Default |
|---|---|---|---|
| n | Yes | Set size | |
| r | No | Selection size |
Changes observed during successful MCP inspections.
Input schema / properties / nAdded value: +{
+ "description": "Set size",
+ "type": "integer"
+}Input schema / properties / rAdded value: +{
+ "description": "Selection size",
+ "type": "integer"
+}Input schema / requiredAdded value: +[
+ "n"
+]Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
With no annotations, the description carries the full burden, and 'Pure CPU, instant' usefully signals a deterministic, side-effect-free local computation. However, it omits edge-case behavior (e.g., r greater than n, or r omitted despite n being the only required parameter) and does not state what is returned when only n is supplied.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Is the description appropriately sized, front-loaded, and free of redundancy?
Two short clauses with zero filler, and the core purpose is front-loaded before the performance note. Every word earns its place.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
For a two-parameter pure function with no output schema, the definition is adequate but thin: it does not clarify whether both nCr and nPr are returned, nor how the optional r (only n is required) is handled. These are small but real gaps an agent would want resolved before calling.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 100%, so n and r are already documented as 'Set size' and 'Selection size'. The description's wording mirrors the schema without adding format, range, or default semantics, so baseline 3 applies.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Does the description clearly state what the tool does and how it differs from similar tools?
The description names a specific verb and resource ('Compute nCr and nPr') plus the inputs ('set size and selection'), so an agent knows exactly what the tool produces. It doesn't explicitly differentiate itself from near-neighbors like factorial or prime, but the operation is distinctive enough that confusion is unlikely.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Does the description explain when to use this tool, when not to, or what alternatives exist?
There is no guidance on when to use this tool versus alternatives such as factorial or math_eval, and no exclusions or prerequisites. The agent must infer the use case entirely from the one-line purpose.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
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