# AI Combinatorics (nCr, nPr) & Binomial Probability Calculator (`ai-tool-combinatorics-probability`)
- **Status**: 200 OK | **Latency**: 1ms | **Cached**: false
- **Primary Authority**: 100% Platform-Native Deterministic AI Core Utility (<1ms)
- **License & Trust**: 100% Platform-Owned Deterministic Algorithm (Commercial Use Allowed) (public_third_party_api)
- **Verified At (UTC)**: 2026-10-27T19:12:30.327Z
- **Data Freshness**: live
## Structured Data
```json
{
  "tool": "ai-tool-combinatorics-probability",
  "n": 49,
  "k": 6,
  "combinations_nCr": 13983816,
  "permutations_nPr": 10068347520,
  "single_ticket_probability": 7.151124e-8,
  "odds_1_in": 13983816
}
```
> **AI Agent Hint**: Agent Data Hub: ask anything via GET /api/v1/ask?q=..., whole tasks via /api/v1/bundles, up to 10 calls via POST /api/v1/batch. Add compact=1 or fields=a,b to save tokens. Docs: /llms.txt