Final answer:
To prevent deadlocks in a system with 6 tape drives where each process may need 3 drives, according to the banker's algorithm principle, the maximum number of processes that can be supported is 2.
Step-by-step explanation:
The scenario where a computer system has 6 tape drives, and there are 'n' processes competing for them, with each process potentially needing up to 3 tape drives. To guarantee a deadlock-free system, we can apply the banker's algorithm principle, which suggests that a system is safe if there are enough resources available to satisfy the maximum demand that could arise from all processes at once. In this case, since each process may require 3 tape drives, we allocate them in such a way that at least one process can always proceed to completion. Therefore, if 'n' processes each need 3 tape drives, the total number of tape drives that the system can safely allocate is 6 (the total number of available tape drives). So, for the system to be deadlock-free, we must have (n-1) processes each able to hold up to 3 drives and the last process able to secure all of its required drives. Mathematically, the system can support 'n' processes if (n-1)*3 < 6, which simplifies to n < 3. Consequently, the maximum number of processes (n) is 2.