Permutations: 17 dogs and 30 cats are competing in an animal show. At the end of the show, the 2 top dogs and 2 top cats will be arranged in a row on a podium for a picture in the following way: 1st place dog, 1st place cat, 2nd place dog, 2nd place cat Without knowing the results of the show, calculate how many different arrangements there could be of pets on the podium