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Home » Shocking Glue Song Lyrics That Will Haunt Your Dreams Forever! - go-checkin.com

Shocking Glue Song Lyrics That Will Haunt Your Dreams Forever! - go-checkin.com

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 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).

📌 Exactly 2: $ \binom{4}{2} \binom{2}{1} = 6 \cdot 2 = 12 $

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