Final answer:
There are 48 different ways for Lorin's pets to be arranged with her two dogs sitting together, by considering the dogs as one unit and accounting for their two possible arrangements within that unit.
Step-by-step explanation:
To determine how many different ways Lorin's pets can be arranged with the condition that her two dogs must sit together, we can use a combinatorial arrangement approach. First, we treat the two dogs as one unit because they have to sit together. This effectively gives us four units to arrange: three cats and one dog unit.
There are 4! (which is 4 x 3 x 2 x 1) ways to arrange four units. This gives us a total of 24 different arrangements for the pets. However, within the dog unit, the two dogs can be arranged in two different ways (dog A can sit on the left or right of dog B). Therefore, we have to multiply 24 by 2, which gives us 48 different ways for Lorin's pets to be arranged.