Question: A linguist studies a corpus of 12 texts, 5 in Old English, 4 in Middle English, and 3 in Early Modern English. If 3 texts are randomly selected, what is the probability that exactly 1 is Old English, 1 is Middle English, and 1 is Early Modern English?
["What Language Historians Uncover: A Statistical Glimpse into England’s Linguistic Evolution", "Curious about how language shifted over centuries? A simple yet revealing exercise involves analyzing a curated corpus of 12 foundational English texts—5 from Old English, 4 from Middle English, and 3 from Early Modern English. When selecting 3 at random, what’s the chance of drawing exactly one from each era? This question isn’t just academic—it reflects growing interest in linguistic heritage, digital humanities, and the evolution of expression in the United States, where language trends often influence education, media, and cultural identity. Researchers and enthusiasts alike seek clarity on representation across eras, much like scholars demand precision when tracing word origins, grammar shifts, and cultural influence in primary sources.", "Understanding the composition of these texts helps contextualize how language was preserved and transformed. With only half the corpus in Old English versus nearly a third in Early Modern English, statisticians and historians uncover patterns of linguistic survival and adaptation. This probabilistic lens offers insight into the rarity—and significance—of encountering markers from each period in a single selection.", "### Why This Language Study Matters Now", "Now more than ever, there’s heightened curiosity about how language shapes culture and identity. Online platforms, academic circles, and public discourse increasingly explore how linguistic evolution reflects social change. A corpus-based study like this taps into broader trends—documenting how England’s spoken and written traditions survived through centuries, influenced by waves of migration, political upheaval, and education reforms.", "For US readers, understanding historical language layers enhances media literacy, especially as digital content blends archaic phrasing with modern usage. Recognizing the rarity of a balanced historical sample encourages deeper engagement with language’s living ecosystem. Whether for academic interest, language learning, or simply satisfying curiosity, this tool serves as both a cognitive exercise and a window into linguistic continuity and transformation.", "### The Actual Probability: A Clear Breakdown", "To compute the probability that a random selection of 3 texts includes one from each era—Old English, Middle English, and Early Modern English—combinatorics offers a precise approach. With 5 Old English, 4 Middle English, and 3 Early Modern English texts, total texts amount to 12.", "The total number of ways to choose 3 texts from 12 is given by the combination formula: \n\[\n\binom{12}{3} = \frac{12 \ imes 11 \ imes 10}{3 \ imes 2 \ imes 1} = 220 \n\]", "Now, calculate the favorable outcomes: one"]
