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Combinations (nCr)

Binomial coefficient nCr = n!/(r!(n-r)!), the number of unordered r-subsets of n. Requires r ≤ n and min(r, n-r) ≤ 10000.

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Host	combinatorics.openverbs.com
Price	$0.004 per call
Network	Base
Paid endpoints listed	5
Calls, last 30 days*	7
Most unique payers on one endpoint (30 days)*	2
Last paid call*	2026-10-08
Tags	combinations ncr, compute combinations, binomial coefficient, ncr api, choose r from n, catalan number, compute catalan, balanced bracket count

* From the public x402 Bazaar index (snapshot 2026-10-18T04:07Z); reported by the facilitator, not measured by us.

Endpoints

URL	Method	Price
`https://combinatorics.openverbs.com/v1/combinations` Binomial coefficient nCr = n!/(r!(n-r)!), the number of unordered r-subsets of n. Requires r ≤ n and min(r, n-r) ≤…	POST	$0.004
`https://combinatorics.openverbs.com/v1/catalan` The n-th Catalan number Cₙ = C(2n, n)/(n+1), counting balanced bracketings, binary trees, and many other structures.…	POST	$0.004
`https://combinatorics.openverbs.com/v1/permutations` Number of ordered arrangements of r items from n, nPr = n!/(n-r)!. Requires r ≤ n and r ≤ 10000.	POST	$0.004
`https://combinatorics.openverbs.com/v1/multinomial` Multinomial coefficient (k1+k2+…)! / (k1! k2! …) — the number of ways to partition n = Σki items into labelled groups…	POST	$0.004
`https://combinatorics.openverbs.com/v1/factorial` Exact factorial n! for 0 ≤ n ≤ 20000, returned as a decimal string with its digit count.	POST	$0.004

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