Multinomial

{
  "asOf": "2026-10-11T14:44:18.681Z",
  "degraded": false,
  "digits": 5,
  "disclaimer": "Screening signal computed from the named public source. Not financial, legal or investment advice; provided as is. Verify at the source before acting.",
  "formula": "11! / (1! x 4! x 4! x 2!)",
  "groupSizes": [
    1,
    4
  ],
  "letters": [
    "Mx1",
    "Ix4",
    "…2 more"
  ],
  "multinomialCoefficient": "34650",
  "notChecked": [
    "dependence between draws (the probability form assumes independent trials with fixed odds, i.e. sampling with replacement)",
    "arrangements with extra constraints such as no two equal letters adjacent"
  ],
  "reasons": [
    "Multinomial coefficient = n! / (k1! k2! ... km!): the number of distinct orderings of n items where equal items are interchangeable."
  ],
  "scientific": null,
  "source": "computed locally (exact big-integer arithmetic)",
  "summary": "11 items in groups 1, 4, 4, 2: 34650 distinct arrangements.",
  "total": 11,
  "verdict": "COUNTED"
}

# bash or zsh: see the payment challenge. Nothing is charged.
curl -sS -g -i 'https://probability-calc.x402tookit.com/multinomial?word=MISSISSIPPI'

# x402 v2 sends the challenge base64-encoded in the PAYMENT-REQUIRED header (v1 sends it in the body).
# To read the header:
curl -sS -g -o /dev/null -D - 'https://probability-calc.x402tookit.com/multinomial?word=MISSISSIPPI' \
  | grep -i '^payment-required:' | cut -d' ' -f2 | tr -d '\r' | base64 --decode

// npm i @x402/fetch @x402/evm viem
import { wrapFetchWithPayment, x402Client } from "@x402/fetch";
import { registerExactEvmScheme } from "@x402/evm/exact/client";
import { privateKeyToAccount } from "viem/accounts";

// Pays at most $0.02 per call.
const client = new x402Client().setSpendControls({ maxAmountPerPayment: "$0.02" });
registerExactEvmScheme(client, { signer: privateKeyToAccount(process.env.EVM_PRIVATE_KEY) });
const pay = wrapFetchWithPayment(fetch, client);

// Not sure it's safe to pay? ToolVet checks it first for $0.005. Pay for that from a separate
// client: this one is capped at $0.02 per payment. GET https://toolvet.app/api/v1/check?url=https%3A%2F%2Fprobability-calc.x402tookit.com%2Fmultinomial
const res = await pay("https://probability-calc.x402tookit.com/multinomial?word=MISSISSIPPI");
console.log(res.status, await res.text());

# pip install "x402[requests,evm]"
import os
from eth_account import Account
from x402 import x402ClientSync
from x402.http.clients import x402_requests
from x402.mechanisms.evm import EthAccountSigner
from x402.mechanisms.evm.exact.register import register_exact_evm_client

# Pays at most $0.02 per call.
client = x402ClientSync().set_spend_controls({"max_amount_per_payment": "$0.02"})
register_exact_evm_client(client, EthAccountSigner(Account.from_key(os.environ["EVM_PRIVATE_KEY"])))

with x402_requests(client) as session:
    res = session.get("https://probability-calc.x402tookit.com/multinomial?word=MISSISSIPPI")
    print(res.status_code, res.text)