I need help understanding please

Problem 2: A dog show will feature 23 participants of three breeds: Akitas, Boxers, and Corgis. The list of participants must include at least 2 dogs of each breed, and there must be at most 9 Akitas, at most 10 Boxers, and at most 7 Corgis. How many possible lists of participants are there? You need to give a complete derivation for the final answer, using the method developed in class. (Brute force listing of all lists