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\(2+1+1+1\) → one zone has 2, three have 1 each
Each of these partitions corresponds to a distinct way to assign the turbine models to indistinct zones, because the zones cannot be distinguished and only the frequency of turbine counts matters.
Thus, there are 6 distinct assignments.
We verify by noting that the number of ways to partition a set of 5 labeled elements into indistinct, possibly empty subsets (with exactly 4 unlabeled bins) is equivalent to the number of integer partitions of 5 into at most 4 parts, which confirms 6.
Therefore, the number of ways is \(\boxed{6}\).
Question:** A climate resilience consultant in LA is analyzing combinations of 3 green infrastructure types (green roofs, permeable pavements, and urban forests) and 5 coastal adaptation strategies (seawalls, elevated buildings, bioswales, flood gates, and managed retreat). How many combinations include exactly 2 green infrastructure types and at least 1 adaptation strategy?
We are to count the number of combinations with exactly 2 out of 3 green infrastructure types **and** at least 1 out of 5 adaptation strategies.
First, compute the number of ways to choose 2 green infrastructure types from 3:
Next, compute the number of ways to choose at least 1 adaptation strategy from 5. The total subsets of 5 strategies is \(2^5 = 32\), and subtracting the empty set gives:
2^5 - 1 = 31