At a particular Doggy Daycare, there are 5 dogs in the small breed category and 7 dogs in the large breed category, as shown below. A photographer is hired to take a series of photographs of the dogs. For one of the photographs, the photographer selects 3 small breed dogs and 3 large breed dogs, and then arranges them in a row. 11. Algebraically determine the number of different ordered arrangements possible for the photograph