# Services from combinatorics.openverbs.com on Zero

> combinatorics.openverbs.com serves 5 paid API services for AI agents, indexed by Zero. Each is callable per call with payment handled by Zero.

Canonical page: https://www.zero.xyz/host/combinatorics.openverbs.com
Live health (JSON, refreshed every minute): https://www.zero.xyz/host/combinatorics.openverbs.com/health.json

## Services

- [Binomial Coefficient Calculator (nCr)](https://www.zero.xyz/c/binomial-coefficient-calculator-ncr-02cc2f33/llms.txt): $0.004/call via x402. Computes the binomial coefficient nCr = n!/(r!(n-r)!), the number of ways to choose r unordered items from a set of n.
- [Combinatorics OpenVerbs Factorial Calculator](https://www.zero.xyz/c/combinatorics-openverbs-factorial-calculator-e61fe949/llms.txt): $0.004/call via x402. Computes the exact factorial n! for any integer 0 ≤ n ≤ 20000, returning the full decimal string and digit count.
- [Catalan Number Calculator](https://www.zero.xyz/c/catalan-number-calculator-b7ecdbb1/llms.txt): $0.004/call via x402. Computes the exact n-th Catalan number Cₙ = C(2n,n)/(n+1) for any n up to 10,000
- [Permutations Calculator (nPr)](https://www.zero.xyz/c/permutations-calculator-npr-e98ab9d1/llms.txt): $0.004/call via x402. Computes the number of ordered arrangements of r items chosen from n distinct items using nPr = n!/(n-r)!
- [Multinomial Coefficient Calculator](https://www.zero.xyz/c/multinomial-coefficient-calculator-c9993b88/llms.txt): $0.004/call via x402. Computes the multinomial coefficient (k1+k2+…)! / (k1! k2! …) — the number of ways to partition n items into labelled groups of specified sizes.

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

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