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rule of product : ウィキペディア英語版
rule of product

In combinatorics, the rule of product or multiplication principle is a basic counting principle (a.k.a. the fundamental principle of counting). Stated simply, it is the idea that if there are a ways of doing something and b ways of doing another thing, then there are a · b ways of performing both actions.〔Johnston, William, and Alex McAllister. ''A transition to advanced mathematics''. Oxford Univ. Press, 2009. Section 5.1〕〔(【引用サイトリンク】title=College Algebra Tutorial 55: Fundamental Counting Principle )
==Examples==
:
\begin
& \underbrace
& & \underbrace \\
\mathrm\ \mathrm\ \mathrm\ \mathrm & \mathrm &
\mathrm\ \mathrm\ \mathrm & \mathrm
\end

:
\begin
\mathrm\ \mathrm\ \mathrm\ \mathrm\ \mathrm & \mathrm. \\
& \overbrace
\end
In this example, the rule says: multiply 3 by 2, getting 6.
The sets and in this example are disjoint sets, but that is not necessary. The number of ways to choose a member of , and then to do so again, in effect choosing an ordered pair each of whose components is in , is 3 × 3 = 9.
As another example, when you decide to order pizza, you must first choose the type of crust: thin or deep dish (2 choices). Next, you choose one topping: cheese, pepperoni, or sausage (3 choices).
Using the rule of product, you know that there are 2 × 3 = 6 possible combinations of ordering a pizza.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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