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,


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.,


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


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

Title rule of product
Canonical name RuleOfProduct
Date of creation 2013-03-22 19:13:02
Last modified on 2013-03-22 19:13:02
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 6
Author pahio (2872)
Entry type Definition
Classification msc 05A05
Classification msc 03-00
Synonym multiplication principle
Related topic CartesianProduct
Related topic Combinatorics
Related topic Cardinality
Related topic Number
Related topic ProductPlanetmathPlanetmath