{ "category": "Math and trigonometry functions", "display_name": "MULTINOMIAL", "entry_kind": "built_in_function", "eval_api": { "method": "POST", "url": "https://handbook.dnacalc.com/api/eval" }, "function_id": "FUNC.MULTINOMIAL", "implementation_state": { "answer_bank": null, "detail": "Recorded: 6 workbook cells.", "dnacalc_commit": "9e1884369a678158dd82d3d74188daf986995e87", "in_catalogue": true, "state": "matches", "state_label": "Matches every recorded Excel answer", "summary": "Matches all 6 recorded answers", "workbook_corpus": { "cells": 6, "matched": 6 } }, "implementations": [ { "commit": "9e1884369a678158dd82d3d74188daf986995e87", "flavour": "excel-compatibility-candidate", "language": "Rust", "name": "CalcFunc", "own_code": [ "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/catalogue/math.rs#L142-L162", "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/ported/factorial_common.rs#L17-L22", "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/ported/multinomial.rs#L21-L31", "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/ported/multinomial.rs#L33-L38", "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/ported/multinomial.rs#L40-L42", "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/ported/multinomial.rs#L44-L46", "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/ported/multinomial.rs#L48-L55", "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/ported/multinomial.rs#L57-L63", "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/ported/multinomial.rs#L65-L73", "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/ported/multinomial.rs#L75-L84", "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/ported/multinomial.rs#L86-L99", "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/ported/multinomial.rs#L101-L109", "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/ported/multinomial.rs#L111-L168", "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/ported/multinomial.rs#L170-L180" ], "repository": "https://github.com/DnaCalc/DnaCalc", "shared_code": [], "source": "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/catalogue/math.rs#L142-L162", "state": "matches", "suite": null, "summary": "Matches all 6 recorded answers" } ], "json_url": "https://handbook.dnacalc.com/api/functions/FUNC.MULTINOMIAL.json", "name": "MULTINOMIAL", "notes": [], "schema": "efh.function-reference/v1", "section_order": [ "what-it-does", "try-it", "quirks", "how-to-implement", "version-differences", "alternatives" ], "sections": { "alternatives": "\n[COMBIN](FUNC.COMBIN.md) chooses one group; [FACT](FUNC.FACT.md) is the factorial primitive; [PERMUT](FUNC.PERMUT.md) distinguishes ordered selections.\n\n\n", "how-to-implement": "\nFor a mathematical integer implementation, start `total=0,result=1`. For each nonnegative integer group size c, multiply the result by `choose(total+c,c)` and increase total by c. Compute each choose with exact integer arithmetic or a cancellation-based recurrence. The example multiplies `choose(2,2)=1`, `choose(4,2)=6`, and `choose(5,1)=5`, yielding thirty. This avoids separately constructing all factorials. The current product also contains log/Lanczos publication candidates and bounded rounding heuristics; the exact-integer recipe is not an identification of those Excel last-bit choices.\n\n\n", "quirks": "\nNegative arguments give `#NUM!`; nonnumeric arguments give `#VALUE!`. The current kernel truncates admitted sizes toward zero. Large factorial intermediates can overflow even when a ratio-based calculation is practical. Numerical publication near large integers needs its own compatibility evidence.\n\n\n", "sources": "\n- [Microsoft: MULTINOMIAL function](https://support.microsoft.com/en-us/excel/functions/multinomial-function), opened 6 November 2026; syntax, documented argument rules and errors.\n- [DnaCalc implementation](https://github.com/DnaCalc/DnaCalc/blob/da3ecc4fb19a3a5529708c311d0e8f05688ac165/crates/calc-func/src/ported/multinomial.rs); implementation steps and the limits identified in the text.\n\n", "try-it": "\n`=MULTINOMIAL(2,2,1)` returns `30`. Five items with two identical A items, two identical B items and one C item have `5!/(2!*2!*1!)=120/4` distinct arrangements.\n\n\n", "version-differences": "\nNo same-input comparison between named Excel builds is recorded for this function here. The documented behaviour below is not a measurement of every Excel release.\n\n\n", "what-it-does": "\n`MULTINOMIAL(number1,[number2],...)` counts arrangements of groups with the supplied sizes: factorial of the total divided by the product of each size’s factorial.\n\n\n" }, "signature": { "display": "MULTINOMIAL(number1, [number2], ...)", "parameters": [ { "description": null, "name": "number1", "optional": false, "repeats": false }, { "description": null, "name": "number2", "optional": true, "repeats": true } ], "trailing_repeats": true }, "sources": { "metadata": { "admission": { "label": "implemented", "reason": null }, "arity": { "max": 255, "min": 1 }, "category": "Math and trigonometry functions", "classification": { "arg_preparation_profile": "ValuesOnlyPreAdapter", "coercion_lift_profile": "Custom", "determinism_class": "Deterministic", "error_collapse_profile": "None", "fec_dependency_profile": "None", "host_interaction_class": "None", "kernel_signature_class": "Custom", "rich_value_usage": "RichBlind", "surface_fec_dependency_profile": "RefOnly", "thread_safety_class": "SafePure", "volatility_class": "NonVolatile" }, "descriptions": { "long": null, "short": "Multinomial coefficient: (a + b + ...)! / (a! b! ...)", "short_source": "dna-calc-own" }, "docs": { "english_description": "Returns the multinomial of a set of numbers", "microsoft_url": "https://support.microsoft.com/en-us/office/multinomial-function-6fa6373c-6533-41a2-a45e-a56db1db1bf6" }, "entry_kind": "built_in_function", "localized_family_names": null, "localized_names": [ { "locale": "ar-SA", "name": "MULTINOMIAL" }, { "locale": "bg-BG", "name": "MULTINOMIAL" }, { "locale": "cs-CZ", "name": "MULTINOMIAL" }, { "locale": "da-DK", "name": "MULTINOMIAL" }, { "locale": "de-DE", "name": "MULTINOMIAL" }, { "locale": "el-GR", "name": "MULTINOMIAL" }, { "locale": "en-AU", "name": "MULTINOMIAL" }, { "locale": "en-GB", "name": "MULTINOMIAL" }, { "locale": "en-US", "name": "MULTINOMIAL" }, { "locale": "es-ES", "name": "MULTINOMIAL" }, { "locale": "et-EE", "name": "MULTINOMIAL" }, { "locale": "fi-FI", "name": "MULTINOMI" }, { "locale": "fr-FR", "name": "MULTINOMIALE*" }, { "locale": "he-IL", "name": "MULTINOMIAL" }, { "locale": "hr-HR", "name": "MULTINOMIAL" }, { "locale": "hu-HU", "name": "SZORHÁNYFAKT" }, { "locale": "id-ID", "name": "MULTINOMIAL" }, { "locale": "it-IT", "name": "MULTINOMIAL" }, { "locale": "ja-JP", "name": "MULTINOMIAL" }, { "locale": "ko-KR", "name": "MULTINOMIAL" }, { "locale": "lt-LT", "name": "MULTINOMIAL" }, { "locale": "lv-LV", "name": "MULTINOMIAL" }, { "locale": "nb-NO", "name": "MULTINOMIAL" }, { "locale": "nl-NL", "name": "MULTINOMIAAL" }, { "locale": "pl-PL", "name": "WIELOMIAN" }, { "locale": "pt-BR", "name": "MULTINOMIAL" }, { "locale": "pt-PT", "name": "POLINOMIAL" }, { "locale": "ro-RO", "name": "MULTINOMIAL" }, { "locale": "ru-RU", "name": "МУЛЬТИНОМ" }, { "locale": "sk-SK", "name": "MULTINOMIAL" }, { "locale": "sl-SI", "name": "MULTINOMIAL" }, { "locale": "sr-Latn-RS", "name": "MULTINOMIAL" }, { "locale": "sv-SE", "name": "MULTINOMIAL" }, { "locale": "th-TH", "name": "MULTINOMIAL" }, { "locale": "tr-TR", "name": "ÇOKTERİMLİ işlevi" }, { "locale": "uk-UA", "name": "MULTINOMIAL" }, { "locale": "vi-VN", "name": "MULTINOMIAL" }, { "locale": "zh-CN", "name": "MULTINOMIAL" }, { "locale": "zh-HK", "name": "MULTINOMIAL" }, { "locale": "zh-TW", "name": "MULTINOMIAL" } ], "signature": { "display": "MULTINOMIAL(number1, [number2], ...)", "parameters": [ { "description": null, "name": "number1", "optional": false, "repeats": false }, { "description": null, "name": "number2", "optional": true, "repeats": true } ], "trailing_repeats": true }, "surface_name": "MULTINOMIAL", "version_marker": null, "xlcall": { "code": "474", "symbol": "xlfMultinomial" } }, "microsoft": "https://support.microsoft.com/en-us/office/multinomial-function-6fa6373c-6533-41a2-a45e-a56db1db1bf6" }, "try_it": { "formula": "=MULTINOMIAL(2,2,1)" }, "url": "https://handbook.dnacalc.com/functions/MULTINOMIAL.html", "variants": [], "versions": [] }