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Multinomial Coefficient & Probability Calculator
x402
Multinomial Coefficient & Probability Calculator is a paid API for AI agents from probability-calc.x402tookit.com, paid per call via x402, $0.02/call, status unknown (last checked 2026-10-29).
Computes the multinomial coefficient (number of arrangements of items with repeats, e.g. MISSISSIPPI) and optionally the multinomial probability given outcome probabilities.
Price / call$0.02
Success—
StatusUnknown
How this service works
Multinomial coefficient (arrangements of repeated items like MISSISSIPPI) and multinomial probability for given odds.
Output
Returns the multinomial coefficient (as a string, possibly in scientific notation), total number of items, the group sizes used, the formula string, a human-readable summary, and optionally the multinomial probability if outcome probabilities were supplied. Also includes metadata like source and an asOf timestamp.
Example use cases
Scrabble word arrangement counting
“How many distinct arrangements of the letters in the word BALLOON are there? I need the multinomial coefficient and the formula.”
Probability of exact outcome mix
“If I have counts 2, 3, 1 and the outcome probabilities are 0.5, 0.3, 0.2, what is the multinomial probability of getting exactly those counts?”
Combinatorics homework problem
“I need to find the number of distinct permutations of the sequence with group sizes 3, 2, 2, 1 — can you compute the multinomial coefficient and show me the formula?”
Technical details
Endpoint
GEThttps://probability-calc.x402tookit.com/multinomial?utm_source=zero.xyzWhen to prefer
Use this endpoint when you need to count distinct arrangements of a multiset (e.g. letters in a word with repeats) or compute the exact multinomial probability for a set of outcome counts given per-outcome probabilities. Prefer this over a general combinatorics endpoint when your problem maps directly to arrangements with repeated items or multinomial distributions.
Side effects
- Missing both 'word' and 'counts' parameters returns an error
- Probabilities that don't sum to 1.0 may produce an error or invalid result
- Non-integer or negative group sizes may be rejected
- Empty or single-character word returns a trivial coefficient of 1
- Very large inputs may exceed numeric precision, returned in scientific notation
Input
Schema · Request body
| Field | Type | Description |
|---|---|---|
| inputrequired | object | |
| output | object |
Tags
x402
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