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📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 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

📌 Each selection of 2 green infrastructure types can be combined with any of these 31 non-empty sets of strategies. So, the total number of valid combinations is:

📌 \binom{3}{2} \times (2^5 - 1) = 3 \times 31 = 93

📌 Thus, the number of combinations is \(\boxed{93}\).

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