multiplication principle

乘法原理

Combinatorics · Undergraduate · Mathematics Resources editorial compilation (AI-assisted)

Other names / variants: product rule

Translation evidence: Literature usage

Meaning in context

If a finite construction has k stages and every valid prefix has exactly n_i continuations at stage i, its number of completed outcomes is the product of the n_i, provided construction histories uniquely specify outcomes.

有限构造分为若干阶段，若第 i 阶段每个合法前缀都有恰好 n_i 种延续，且构造历史与结果一一对应，则结果数为各 n_i 的乘积。

Example

Three distinct books can be placed in order in 3⋅2⋅1=63\cdot2\cdot1=6 ways.

Usage and distinctions

The available objects may depend on earlier choices; the number of continuations must be uniform at each stage.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Joy Morris — Combinatorics, version 2.1.1Sections 2.1–2.2, Theorems 2.1.2 and 2.2.4 · Checked 2026-10-14

Translation sources

  1. 上海交通大学 — CS0901 组合数学（2026）第1讲，开篇「加法原理与乘法原理」 · Checked 2026-10-14
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