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Math and Statistics – Combinatorics Calculator
x402
Math and Statistics – Combinatorics Calculator is a paid API for AI agents from math-stats.x402tookit.com, paid per call via x402, $0.02/call, status unknown (last checked 2026-10-30).
Computes exact combinatorial counts—factorial, combinations, permutations, repetition variants, derangements, and Catalan numbers—as arbitrary-precision big integers.
Price / call$0.02
Success—
StatusUnknown
How this service works
Exact counts: factorial, combinations, permutations, with repetition, derangements and Catalan numbers, as big integers.
Output
A JSON object containing exact big-integer string values for factorial, combinations (n choose k), permutations, combinations with repetition, permutations with repetition, derangements, and Catalan number for the given n (and optional k). Also includes the number of digits in n! and a scientific-notation representation. Values are returned as strings to preserve full precision for very large numbers.
Example use cases
Lottery odds exact calculation
“How many 5-card hands can be dealt from a standard 52-card deck? Give me the exact combination count, not an approximation.”
Seating arrangement count
“In how many ways can 10 people be seated at a table such that none of them sits in their originally assigned seat? Give me the exact derangement count for n=10.”
Password space enumeration
“I have a character set of 62 characters and want passwords of length 8 with repetition allowed—what is the exact permutations-with-repetition count?”
Technical details
Endpoint
GEThttps://math-stats.x402tookit.com/combinatorics?utm_source=zero.xyzWhen to prefer
Choose this endpoint when you need exact, arbitrary-precision combinatorial counts rather than floating-point approximations. It is ideal for probability problems, cryptographic key-space analysis, card game odds, permutation puzzles, or any combinatorics homework where precision matters. Prefer it over a general-purpose math library call when you need all major combinatorial quantities (factorial, C(n,k), P(n,k), with-repetition, derangements, and Catalan) in a single request.
Side effects
- Missing required parameter n returns an error
- n out of range (negative or > 2000) returns a validation error
- k out of valid range for the chosen operation returns a null or error for that field
- Non-integer values for n or k cause a schema validation failure
- Combinatorial results for very large n may still succeed but produce extremely long big-integer strings
Input
Schema · Request body
| Field | Type | Description |
|---|---|---|
| inputrequired | object | |
| output | object |
Tags
x402
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