Solution: First, compute the total number of ways to choose 3 species: $\binom{20}{3} = 1140$. The number of favorable outcomes is $\binom{10}{2} \cdot \binom{6}{1} = 45 \cdot 6 = 270$. The probability is:

["Understanding Probability: Calculating Successful Outcomes When Selecting Species", "When analyzing complex biological or ecological systems, combinatorics plays a vital role in answering probability questions. A classic example involves calculating the chance of selecting specific species from a diverse population. Consider the scenario:", "First, compute the total number of ways to choose 3 species from 20 different species:\n[\n\binom{20}{3} = \frac{20 \ imes 19 \ imes 18}{3 \ imes 2 \ imes 1} = 1140\n]\nThis total count represents all possible groups of 3 species that could be selected from the entire pool.", "Next, suppose we’re interested in a specific favorable outcome—such as selecting exactly 2 species from one subgroup and 1 from another. For instance, choosing 2 species from 10 target species and 1 species from a complementary 6 species:\n[\n\binom{10}{2} \cdot \binom{6}{1} = \frac{10 \ imes 9}{2} \cdot 6 = 45 \cdot 6 = 270\n]\nThis product gives the number of favorable combinations where exactly 2 species come from one defined category and 1 from another.", "To find the probability of this favorable selection occurring among all possible groups, divide the favorable outcomes by the total outcomes:\n[\n\ ext{Probability} = \frac{270}{1140} = \frac{9}{38} \approx 0.2368 \quad \ ext{(about 23.68%)}\n]", "This streamlined approach—using combinations to compute total and favorable selections—forms a foundational technique in probability theory. It enables precise calculations essential for ecological modeling, genetics, conservation planning, and beyond. Understanding how to compute these values not only strengthens mathematical reasoning but also supports evidence-based decision-making in biological sciences.", "Whether analyzing biodiversity, population genetics, or ecosystem diversity, using combinatorial methods offers clarity and accuracy. Mastering these calculations empowers researchers and students alike to interpret data with confidence."]