How many 5-digit positive integers have digits that are strictly increasing (i.e., each digit less than the next), using only the digits 0, 1, 2, 3, 4, 5?

["How Many 5-Digit Positive Integers Have Strictly Increasing Digits Using Only 0–5?", "What if a simple rule created a precise count of valid 5-digit numbers—ones where each digit gets strictly larger than the one before, using only the digits 0, 1, 2, 3, 4, and 5? That number might surprise you, and its calculation reveals both mathematical elegance and growing curiosity online.", "Data shows increasing interest in number patterns and combinatorial puzzles, especially among users exploring numerical constraints. This particular question—《How many 5-digit positive integers have digits that are strictly increasing using only 0, 1, 2, 3, 4, 5?》—blends logic, digital literacy, and everyday pattern recognition, making it a steady topic across math enthusiasts, educators, and curious browsers.", "### Why This Question Is Resonating in 2024", "Across the U.S., users engage deeply with logic-based queries that connect simple rules to measurable outcomes. Social trends highlight growing attention to structured challenges, digital literacy puzzles, and educational exploration—especially in mobile-first browsing environments. Quantum curiosity around "how many" solutions exists in coding, finance, and data science; this digit-constrained number puzzle fits naturally into those interests without sensationalism.", "Users searching for precise counts often seek clarity beyond guesswork—wanting verified answers rooted in counting principles. This query reflects a trend toward seeking structured, trustworthy data behind seemingly playful number puzzles.", "### How Closed-Range Increasing Digits Generate Unique Numbers", "A strictly increasing sequence means each digit must be greater than the one preceding it. Since digits range from 0 to 5 and we need 5-digit numbers (first digit ≠ 0), the challenge becomes selecting 5 distinct digits from 0 to 5, then arranging them in ascending order—only one valid order exists per combination.", "We select 5 different digits from the set {0, 1, 2, 3, 4, 5}, totaling 6 digits. The number of ways to choose 5 from 6 is given by the combination formula:", "\[\n\binom{6}{5} = 6\n\]", "Each such"]