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Binomial Coefficient Calculator (nCr)
x402
Binomial Coefficient Calculator (nCr) 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 binomial coefficient nCr = n!/(r!(n-r)!), the number of ways to choose r unordered items from a set of n.
Price / call$0.004
Success—
StatusUnknown
How this service works
Binomial coefficient nCr = n!/(r!(n-r)!), the number of unordered r-subsets of n. Requires r ≤ n and min(r, n-r) ≤ 10000.
Output
Returns the exact integer value of the binomial coefficient nCr = n!/(r!(n-r)!), representing the number of unordered r-subsets of an n-element set. The result is a large exact integer (as a decimal string for large values), with constraints that r ≤ n and min(r, n-r) ≤ 10000.
Example use cases
Lottery odds combination count
“How many different ways can 6 numbers be chosen from 49 in a lottery draw? I need the exact number of possible combinations, C(49,6).”
Card hand probability setup
“I'm calculating poker probabilities — how many distinct 5-card hands are possible from a standard 52-card deck? Give me C(52,5).”
Committee selection enumeration
“Our organization has 30 members and we need to form a committee of 8. How many different committees are possible? Calculate C(30,8) for me.”
Technical details
Endpoint
POSThttps://combinatorics.openverbs.com/v1/combinationsWhen to prefer
Choose this endpoint when you need the exact count of unordered selections (combinations) of r items from n, e.g. for probability calculations, lottery odds, or combinatorial enumeration. Prefer this over the permutations endpoint (nPr) when order does not matter. Use instead of factorial endpoint when you specifically need the binomial coefficient rather than a raw factorial.
Side effects
- r > n: invalid input since you cannot choose more items than exist in the set
- min(r, n-r) > 10000: exceeds computation limit
- n > 1000000: n exceeds maximum allowed value
- non-integer or negative inputs: inputs must match pattern ^\d+$
- malformed request body: missing required fields n or r
Input
Schema · Request body
| Field | Type | Description |
|---|---|---|
| inputrequired | object |
Tags
x402
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