Numerical answer
How many four-digit numbers with all digits distinct are divisible by 5?
Show answer and solution
Answer: 952
The last digit must be 0 or 5.
Last digit 0: first digit 9 choices (1–9), second 8, third 7 → 9 × 8 × 7 = 504.
Last digit 5: first digit cannot be 0 or 5 → 8 choices; second digit: any of the remaining 8 (0 now allowed); third: 7 → 8 × 8 × 7 = 448.
Total = 504 + 448 = 952.
Tip: Always fix the restricted positions (units digit, leading digit) first, and split into cases when the restrictions interact (here, whether 0 is already used).
Last digit 0: first digit 9 choices (1–9), second 8, third 7 → 9 × 8 × 7 = 504.
Last digit 5: first digit cannot be 0 or 5 → 8 choices; second digit: any of the remaining 8 (0 now allowed); third: 7 → 8 × 8 × 7 = 448.
Total = 504 + 448 = 952.
Tip: Always fix the restricted positions (units digit, leading digit) first, and split into cases when the restrictions interact (here, whether 0 is already used).
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