Combinatorial testing can significantly reduce the number of tests needed to cover all variable combinations by focusing on pairwise combinations. The document discusses pairwise testing, which aims to test all combinations of each pair of input parameters. This catches a high percentage of errors while dramatically reducing the number of required test cases. Tools like PICT can automatically generate optimal pairwise test suites. The document provides an example showing PICT reducing 96 potential test cases for a car ordering application down to just 8 test cases.