If you are in a situation where you have two make two consecutive choices and the first one can be selected from n alternatives and the second can be selected from m alternatives the total number of possible combinations is n*m. This can be easilty understood since for each of the n choices of A there are m possibilities to select the second item.
Ex: Då man väljer en Golf cabriolet kan man välja mellan fyra lackfärger, fyra klädselfärger och fyra fyra motorer.
Hur många olika varianter av Golf cabriolet är teoretiskt möjliga?
Svar: 4 * 4 * 4 = 64 st.enligt multilikationsprincipen.
Ex. Determine the number of sub-sets to a set consisting of 10 elements.
A subset of a set M can be determined by going through the elementsof M, one at a time, and determines whether it belongs to the subset or not. For each element there are then 2 options: either it belongs to the subset or it doesn’t. Hence the totoal number of possibilities is 210.
Therefore the total number of subsets for the set M is 210.
In the general case when M has n elements the number of subsets is 2n.
On the other hand if you are are going to choose one item from either subset A or from subset the number of possibilities you can choose from is obviously m + n.