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Thus, the number of ways is $\boxed{301}$.
Question: A software developer is training a neural network with 4 distinct image filters. How many ways can they assign these filters to 2 identical processing modules, allowing for empty modules?
Solution: Since the modules are indistinguishable and empty modules are allowed, the number of ways is the sum of Stirling numbers of the second kind for partitions into 1 and 2 non-empty subsets:

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