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Multinomial Coefficient Calculator
x402
Multinomial Coefficient Calculator is a paid API for AI agents from combinatorics.openverbs.com, paid per call via x402, $0.004/call, status unknown (last checked 2026-09-14).
Computes the multinomial coefficient (k1+k2+…)! / (k1! k2! …) — the number of ways to partition n items into labelled groups of specified sizes.
Price / call$0.004
Success—
StatusUnknown
How this service works
Multinomial coefficient (k1+k2+…)! / (k1! k2! …) — the number of ways to partition n = Σki items into labelled groups of the given sizes. The sum must be ≤ 20000.
Output
Returns the exact multinomial coefficient as a large integer (likely as a decimal string given the potential for very large values), representing the number of distinct ways to partition n = Σki items into the specified labelled groups.
Example use cases
Team distribution planning
“I have 15 employees and I want to split them into three project teams of 5, 6, and 4 people — how many distinct ways can I do that? Calculate the multinomial coefficient for group sizes 5, 6, and 4.”
Letter arrangement counting
“How many distinct arrangements are there of the word MISSISSIPPI? That's groups of 1 M, 4 I's, 4 S's, and 2 P's — compute the multinomial coefficient for group sizes 1, 4, 4, 2.”
Probability denominator for large partition
“For a probability calculation, I need the multinomial coefficient for partitioning 100 items into groups of 30, 25, 20, 15, and 10 — can you compute that exact value?”
Technical details
Endpoint
POSThttps://combinatorics.openverbs.com/v1/multinomialWhen to prefer
Choose this endpoint when you need the exact multinomial coefficient for partitioning items into three or more labelled groups. For two-group partitions, the binomial coefficient endpoint on the same service may be simpler. For ordered arrangements, use the permutation endpoint. This endpoint handles sums up to 20000, making it suitable for large combinatorial problems that would overflow standard integer arithmetic.
Side effects
- Sum of group sizes exceeds 20000 — returns an error
- Empty or missing groups array — validation error
- Non-integer or negative group sizes — schema rejection
- Exceeds 256 groups limit — rejected by maxItems constraint
- Network timeout on very large computations
Input
Schema · Request body
| Field | Type | Description |
|---|---|---|
| inputrequired | object |
Tags
x402
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