Bear,
A service tag (at least in Dell's case) is the serial number of the entire piece of hardware that was sold, known as the "computer". That's not to say each component (hard drive, motherboard, monitor) don't have a serial number of their own, but most people wouldn't report their hard drive's serial number to police. Just like a car, the engine and transmission may have a different serial number than the VIN for the whole car.
Your "so very few" numbers comment... think of license plates. Most of them (here in FL) are only 6 characters but we have millions of cars on the road with unique plates.
For example, if you convert service tag 5RFDP01 into a number, it comes out as 12,542,331,601. Yes, that's 12 billion.
There are 36 combinations for each character/digit in the service tag... about 78 million unique combinations.
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