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If an event A has n possible outcomes and an event B has m possible outcomes, then the total number of different outcomes for A and B combined is n * m. This principle is used to find the number of possible outcomes for a combination of independent events.
This happens for each of the n different ways in which the process can be started. Therefore, there are n* m different ways of completing the process. This is a generic argument that can be applied in multiple scenarios. For example, the following diagram shows the different choices of the notebooks that a store sells.
In this example, the store sells 2 types of notebooks, one with a ring binding and one with a spiral binding. Each notebook type comes in 3 different colors: blue, red, and green. According to the Fundamental Counting Principle, there are 6 different outcomes for which notebook a customer may buy. 2* 3 = 6 It should be noted that this is an informal justification and should not be taken as a formal proof.
There are still 2 types of notebooks and a total of 3 colors for the ring-bound notebooks. However, the possible number of different notebooks a customer may buy is not 2* 3= 6. Rather, it is 4. This happens because the number of possible colors of the notebook now depends on the type of notebook.