Fifteen new corvettes are randomly allocated to 3 dealerships with each dealership re- ceiving 5 corvettes. Three of the corvettes have maladjusted front brakes. Find the probability that each dealership gets a car needing a brake adjustment. [First find the number of ways to allocate 5 corvettes to each dealership, by thinking sequentially: choose 5 of 15 corvettes to go to dealership #1, followed by choosing 5 of 10 remaining corvettes to dealership #2, followed by choosing 5 of 5 corvettes to go to dealership #3... multiply these combinations to the total of such choices. Then, find the number of ways to allocate 5 corvettes to each dealership so that each dealership gets one defective corvette (i.e., with maladjusted front brakes)... again think sequentially: pick 1 of the 3 defective corvettes and 4 of the 12 non-defective corvettes to go to dealership #1; out of the remaining corvettes, pick 1 defective and 4 non-defective corvettes to go to dealership #2; and then out of the remaining corvettes, pick 1 defective and 4 non-defective corvettes to go to dealership #3.]