If we had combined all the partitions we derived from the substringsBetween program, we would have ended up with 320 tests. This number is even larger for more complex problems. Combinatorial testing is an entire area of research in software testing; I will not dive into the techniques that have been proposed for such situations, but I will provide you with two pragmatic suggestions.
First, reduce the number of combinations as much as possible. Testing exceptional behavior isolated from other behaviors (as we did in the example) is one way to do so. You may also be able to leverage your domain knowledge to further reduce the number of combinations.
Second, if you are facing many combinations at the method level, consider breaking the method in two. Two smaller methods have fewer things to test and, therefore, fewer combinations to test. Such a solution works well if you carefully craft the method contracts and the way they should pass information. You also reduce the chances of bugs when the two simple methods are combined into a larger, more complex one.
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