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university of arkansas at monticello - GetMeFoodie

📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 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 $

📌 Exactly 3: $ \binom{4}{3} = 4 $

📌 Total favorable: $ 12 + 4 = 16 $.

📌 Probability: $ \frac{16}{20} = \frac{4}{5} $.

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