A math problem database has three different categories of problems with $30$, $40$, and $45$ questions in each category. For any test, one problem from each of the three categories is selected. How many ways can the three problems be selected? 
Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Principle of Multiplication