In practice, it is usually impossible to test all parameter combinations for real life applications. Say, you have 10 different parameters of a tax advice software where each parameter is true of false. Enumerating all parameter combinations leads to 3,628,800 test cases already. So, testing can always check a few combinations, only.
But, when the software finally goes public, I often see that rare usage patterns occur which have never been tested. There is a neat trick by a research group at NIST: Automated Combinatorial Testing for Software. Richard Kuhn, Raghu Kacker and Yu Lei observed that most errors occur by a change of one or two parameters, only. A two way test with 10 parameters can be done in 10 test cases. Even a 4-way test, where a specific set of 4 parameters is required to trigger a bug, is easy to do with 42 test cases.
