|
|
| Line 1: |
Line 1: |
| {{one source|date=November 2011}}
| | Oscar is how he's called and he totally enjoys this name. Years in the past we moved to Puerto Rico and my family members enjoys it. I utilized to be unemployed but now I am a librarian and the wage has been truly fulfilling. One of the things she enjoys most is to read comics and she'll be starting some thing else alongside with it.<br><br>My blog; [http://tomport.ru/node/19667 over the counter std test] |
| In [[combinatorics]], the '''rule of product''' or '''multiplication principle''' is a basic [[combinatorial principles|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.<ref>http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut55_count.htm</ref>
| |
| | |
| :<math>
| |
| \begin{matrix}
| |
| & \underbrace{ \left\{A,B,C\right\} }
| |
| & & \underbrace{ \left\{ X,Y\right\} } \\
| |
| \mathrm{To}\ \mathrm{choose}\ \mathrm{one}\ \mathrm{of} & \mathrm{these} &
| |
| \mathrm{AND}\ \mathrm{one}\ \mathrm{of} & \mathrm{these}
| |
| \end{matrix}
| |
| </math>
| |
| | |
| <!-- extra blank space between two [[TeX]] displays for improved legibility -->
| |
| | |
| :<math>
| |
| \begin{matrix}
| |
| \mathrm{is}\ \mathrm{to}\ \mathrm{choose}\ \mathrm{one}\ \mathrm{of} & \mathrm{these}. \\
| |
| & \overbrace{ \left\{ AX, AY, BX, BY, CX, CY \right\} }
| |
| \end{matrix}</math>
| |
| | |
| In this example, the rule says: multiply 3 by 2, getting 6.
| |
| | |
| The sets {''A'', ''B'', ''C''} and {''X'', ''Y''} in this example are disjoint, but that is not necessary. The number of ways to choose a member of {''A'', ''B'', ''C''}, and then to do so again, in effect choosing an [[ordered pair]] each of whose components is in {''A'', ''B'', ''C''}, is 3 × 3 = 9.
| |
| | |
| In [[set theory]], this multiplication principle is often taken to be the definition of the product of [[cardinal number]]s. We have
| |
| | |
| :<math>|S_{1}|\cdot|S_{2}|\cdots|S_{n}| = |S_{1} \times S_{2} \times \cdots \times S_{n}| </math>
| |
| | |
| where <math> \times </math> is the [[Cartesian product]] operator. These sets need not be finite, nor is it necessary to have only finitely many factors in the product; see [[cardinal number]].
| |
| | |
| == example ==
| |
| | |
| When you decide to order pizza, you must first choose the type of crust: thin or deep dish (2 choices). Next, you choose the 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.
| |
| | |
| == See also ==
| |
| | |
| *[[Combinatorial principle]]
| |
| *[[Rule of sum]]
| |
| | |
| == References ==
| |
| {{Reflist}}
| |
| | |
| [[Category:Combinatorics]]
| |
| | |
| {{Combin-stub}}
| |
| | |
| [[fi:Todennäköisyysteoria#Tuloperiaate ja summaperiaate]]
| |
Oscar is how he's called and he totally enjoys this name. Years in the past we moved to Puerto Rico and my family members enjoys it. I utilized to be unemployed but now I am a librarian and the wage has been truly fulfilling. One of the things she enjoys most is to read comics and she'll be starting some thing else alongside with it.
My blog; over the counter std test