Please tell me how to correctly calculate the number of combinations in such a task: There are 3 machines, 3 possible technological processes by which the product can be produced, 3 tooling options for each machine. Each operation of those. The process is performed on a single machine.
It seemed to me that this is a product of factorials 3! * 3! * 3! * 3 !. But something tells me that everything is more complicated. Thank you very much in advance!
Machine A , it has three tooling - 1, 2, 3 to perform three operations a, b, c
A1a-A1b-A1c - three possible options for operations with equipment 1
Add two more snap-ins: 3 + 2 * 3 = 9 options for machine A
For three machines: 9 * 9 * 9. Simply!
It would be nice ... Since there are no restrictions in the task (on using snap-ins, on performing operations), then ...
We have 9 equipment, 9 operations as well (3 * 3 tech process). Specific equipment for a specific operation. Yes? Technologists could skip pairs and not know how to, therefore, on which machine which equipment would fit and what operation would be performed on it, no one knows. It means that for one machine A: 9 * 9 = 81 variants of using all 9 snap-ins and performing possible 9 operations.
We have three machines: 81 * 81 * 81
----------------------------- Machines - x , snap on the machine - y , technical processes - z
Total snap-ins Y = y * x (for snap-ins for each machine)
Total operations Z = z * x (each operation of the technical process is performed on one machine)
f=(Y*Z)^x=(y*z*x^2)^x 
Source: https://ru.stackoverflow.com/questions/567768/
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