Solution: We are to count the number of distinct sequences of 12 blocks, where there are 5 red (R), 4 blue (B), and 3 green (G), and blocks of the same color are indistinguishable. This is a permutation of a multiset:

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**How Many Unique Patterns Emerge from 12 Blocks? A Statistical Insight for Curious Learners** In a world increasingly shaped by data and probability, a simple yet fascinating question surfaces: how many unique sequences can arise from arranging 12 colored blocks—5 red, 4 blue, and 3 green—where blocks of the same color look identical? This isn’t just a math puzzle; it’s a window into combinatorics shaping modern decision-making, product design, and trend analysis across the US digital landscape. While color-coded patterns might seem abstract, their math underpins real-world applications—from inventory patterns to product customization and algorithmic design. With so many distinct arrangements possible, understanding this permutation reveals how rarity and variation manifest even in seemingly simple systems. This exploration dives into the science behind counting distinct sequences, answers common questions readers have, and explains why this calculation matters beyond abstract math—especially in fields like UX design, branding, and data-driven strategy.