In a study about college students, students are classified according to their department and preference of language course. If there are 10 different departments and 5 different language courses, in how many different ways can a student be classified? According to the basic principle of counting, it follows that there are in total 10.5=50 different possible classifications.

In a study about employess, employees are classified according to the department they work in and their preference of training courses. If there are 12 different departments and 7 different courses, according to the basic principle of counting, itf ollows that there are in total 12.7=84 different possible classifications.