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What do people mean when refer to the “combinatorial explosion” of the testing cases?

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What do people mean when refer to the “combinatorial explosion” of the testing cases?

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This refers to the fact that even for a simple product functionality it is virtually and practically impossible to test all the possible combinations of external parameters, input values, settings and internal states. The reason is that the combination of possible test cases would be for all practical purposes equivalent to infinity. Even though this makes the Product Testing a seemingly impossible task, in fact it stresses the point for applying the Product Testing discipline from years of experience. This experience is what allows to choose a reasonable number of test cases to obtain nearly full coverage of the product functionality.

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