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Home » Addiere 7: 4x = 28 - Dachbleche24

Addiere 7: 4x = 28 - Dachbleche24

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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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:

📌 S(4, 1) + S(4, 2) = 1 + 7 = 8

📌 Here, $ S(4, 1) = 1 $ (all filters in one module) and $ S(4, 2) = 7 $ (ways to split 4 filters into 2 non-empty groups). Thus, the total is $\boxed{8}$.

📌 Question: An angel investor is evaluating 6 biotechnology startups. What is the probability that at least 2 of the 3 randomly selected startups focus on gene editing, given that 4 of the 6 startups specialize in this area?

📌 Solution: Total ways to choose 3 startups: $ \binom{6}{3} = 20 $.

📌 Favorable cases: At least 2 gene-editing startups include (2 or 3).

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