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Home » \[ \frac1f = \frac1v - \frac1u \] - SUpost

\[ \frac1f = \frac1v - \frac1u \] - SUpost

📅 July 6, 2026 👤 scraface

Jul 06, 2026

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📌 Actually, better approach: compute valid combinations directly where each category is represented.

📌 A chemical engineer is testing 12 new sustainable solvents: 5 are water-based, 4 are bio-based, and 3 are ionic. If 6 solvents are selected at random, what is the probability that at least one solvent from each type is included?

📌 We compute the probability that a random selection of 6 solvents from 12 (5 water, 4 bio, 3 ionic) contains at least one from each type.

📌 Total number of ways to choose 6 solvents:

📌 Use complementary counting: subtract cases missing at least one type.

📌 Therefore, number of favorable outcomes:

📌 Simplify: divide numerator and denominator by 7:

📌 A sustainable industrial process uses 3 types of catalytic materials: 7 carbon-based, 5 ceramic, and 4 polymer-based. If 8 materials are selected at random, what is the probability that the selection includes at least two polymer-based catalysts?

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