An engineer is testing 10 new eco-friendly solvents: 4 volatile, 4 semi-volatile, and 2 non-volatile. If 6 solvents are selected at random, what is the probability that exactly one is non-volatile and at least two are volatile?

Mon, 04 May 2026 07:10:38 +0000

**Why Data-Driven Solvent Selection Matters: A Mathematical Insight into Eco-Friendly Innovation** In a rapidly evolving landscape where sustainable chemistry is gaining momentum, one engineer’s rigorous testing of 10 new eco-friendly solvents has sparked quiet interest across technical and environmental communities. With four volatile, four semi-volatile, and two non-volatile options in the sample, a focused analysis explores a specific combinatorial question: what’s the likelihood, using pure probability, that selecting six solvents at random results in exactly one non-volatile and at least two volatile? This isn’t just a math puzzle—it reflects strategic decision-making in real-world innovation, where balance between stability, safety, and sustainability drives selection. As industries shift toward greener practices, such probabilistic insights help engineers and decision-makers quantify risk and feasibility in material choice. This exploration offers clarity for curiosity-driven readers navigating the complexity of modern chemical development. **Why This Problem Is Trending in Engineering and Sustainability Circles** The testing of new solvent formulations reflects a broader national pivot toward safer, environmentally responsible industrial materials. With rising demand for low-toxicity, biodegradable alternatives, companies are evaluating performance and safety through rigorous statistical models. When selecting six solvents from a limited set—especially with distinct categories defined by volatility—engineers use probabilistic reasoning to predict outcomes without relying solely on trial and error. This scenario mirrors real challenges in R&D: maximizing likely success while managing uncertainty. The convergence of environmental responsibility and data-informed testing explains growing interest in solving such combinatorial puzzles—an opportunity for professionals and informed readers to understand the science behind green innovation. **Understanding the Probability: Exactly One Non-Volatile and At Least Two Volatile** We begin with 10 solvents: 4 volatile (V), 4 semi-volatile (S), and 2 non-volatile (N). When choosing 6 at random, the goal is to compute the probability that precisely one solvent is non-volatile and at least two are volatile. This requires careful combinations: selecting one N from two, and then ensuring the remaining five come mostly from volatile and semi-volatile—with at least two classified