How does the Bridge pattern prevent the class explosion that happens when you model every combination of two independent hierarchies as its own class?

Modeling every combination directly, such as one class per remote-type-and-device-type pairing, needs N times M classes for N remote types and M device types -- 50 classes for just 5 remotes and 10 devices, with logic duplicated across every class sharing a device or a remote type. Bridge fixes this by recognizing that the two dimensions are genuinely independent and should never have been combined into one hierarchy at all. It splits them into two separate hierarchies -- an abstraction hierarchy and an implementation hierarchy -- and connects them through one composition reference held by the abstraction. That turns the class count from N times M into N plus M, which is 15 for the same 5-and-10 example, and the gap only widens as either dimension keeps growing.