What is the minimum number of four digits formed by using the digits $2$, $4$, $0$, $7$?

### Concept & Logic To form the smallest possible number from a given set of unique digits, arrange the digits in ascending order. However, a number cannot have $0$ as its leading digit, so the smallest non-zero digit must take the first position. ### Step-by-Step Solution **Given:** The digits are $2, 4, 0, 7$. We need a 4-digit number. **Calculation:** 1. Sort the given digits in purely ascending order: $0, 2, 4, 7$. 2. Placing $0$ at the beginning ($0247$) creates a 3-digit number. Therefore, swap the $0$ with the next smallest digit ($2$). 3. The leading digit becomes $2$. The $0$ immediately follows it. 4. Place the remaining digits in ascending order: $4$, then $7$. 5. The resulting sequence is $2047$. ### Exam Strategy & Shortcut First, eliminate any option that doesn't use the exact set of given digits (e.g., Option B uses two $2$s). Out of the remaining valid permutations ($2047$, $2407$, $2470$), simply identify the numerically smallest value. ### Common Pitfall The most common mistake is ignoring the rule that 4-digit numbers cannot start with $0$, leading students to search for $0247$. When it's missing, they might panic and guess randomly. ### Final Answer Therefore, the correct answer is **2047**.