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单词 RuleOfProduct
释义

rule of product


If a process A can have altogether m different results and another process B altogether n different results, then the two processes can have altogether mn different combined results.  Putting it to set-theoretical form,

card(A×B)=mn.

The rule of product is true also for the combinationMathworldPlanetmathPlanetmath of several processes:  If the processes Ai can have ni possible results (i=1, 2,,k), then their combined process has n1n2nk possible results.  I.e.,

card(A1×A2××Ak)=n1n2nk.

Example.  Arranging n elements, the first one may be chosen freely from all the n elements, the second from the remaining n-1 elements, the third from the remaining n-2, and so on, the penultimate one from two elements and the last one from the only remaining element; thus by the rule of product, there are in all

n(n-1)(n-2)21=n!

different arrangements, i.e. permutationsMathworldPlanetmath, as the result.

Titlerule of product
Canonical nameRuleOfProduct
Date of creation2013-03-22 19:13:02
Last modified on2013-03-22 19:13:02
Ownerpahio (2872)
Last modified bypahio (2872)
Numerical id6
Authorpahio (2872)
Entry typeDefinition
Classificationmsc 05A05
Classificationmsc 03-00
Synonymmultiplication principle
Related topicCartesianProduct
Related topicCombinatorics
Related topicCardinality
Related topicNumber
Related topicProductPlanetmathPlanetmath
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更新时间:2025/5/4 8:34:16