Theoretical combinations and a key-control plan

A theoretical classroom model gives a training key five independent cut positions and six allowable depth values at each position. The task explicitly ignores adjacent-cut restrictions, reserved combinations and other manufacturer constraints for the arithmetic portion. A trainee multiplies five by six and claims there are thirty combinations. Another correctly finds a larger theoretical number but treats every mathematical sequence as a suitable key in an actual master-key system. The instructor also provides an authorization schedule showing that different users should access different training cylinders. Students must calculate the simplified count and distinguish mathematical possibility, practical usability and authorized access. No customer bitting, protected code database or real building access schedule is provided, and the exercise does not establish a usable master-key design.