Exhaustive testing is a test approach in which all possible data combinations are used for testing. Exploratory testing includes implicit data combinations present in the state of the software/data at the start of testing.
Consider an application in which a password field that accepts 3 characters, with no consecutive repeating entries. Hence, there are 26 * 26 * 26 input permutations for alphabets only. Including special characters and standard characters, there are much more combinations. So, there are 256 * 256 * 256 input combinations.