answer a question with explanation

3. [10 pts] Local car enthusiast Steph wants to organize the cars in her garage. (a) Her garage contains 289 parking spots arranged in a 17 x 17 grid. Each parking spot can hold one car. She has 17 red Ferraris, as they are her favorite type of car. Each Ferrari is indistinguishable from every other. She wants to park these 17 Ferraris in her garage for safekeeping, arranging them such that no two cars are in the same row or column. How many ways can she do this? (b) Steph has a second floor of the garage with the exact same dimensions, 289 compartments arranged in a 17 x 17 grid. She asks you to help her arrange 17 of her cars that are not Ferraris. These 17 cars are all distinct. Given that she also wants these arranged such that no two cars are in the same row or column, how many ways are there to arrange her second garage