No Repeat Digits

What this digit-distinctness probability question tests

This is an easy probability question commonly used in quant interviews to assess whether candidates can count outcomes carefully and set up a basic probability ratio. It rewards clear enumeration and attention to edge cases rather than advanced techniques.

To solve problems of this type, you identify the total number of outcomes in your sample space, then count how many satisfy the constraint (in this case, all digits being different from one another). The key is handling numbers of different lengths systematically—single-digit, two-digit, three-digit, and four-digit cases each obey slightly different rules. Many candidates make mistakes by either forgetting to exclude leading zeros or by misapplying the multiplication principle across digit positions.

• Counting distinct arrangements with and without replacement
• Handling constraints like leading zeros
• Partition of sample space by number of digits