Question:
The number of positive integers less than 10000 which contain the digit 5 at least once is
The number of positive integers less than 10000 which contain the digit 5 at least once is
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To count "at least once" digit problems, use complementary counting: Total - numbers that do not contain the digit.
Updated On: Jun 4, 2025
- 3168
- 3420
- 3439
- 5832
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The Correct Option is C
Solution and Explanation
Total positive integers \(<10000 \): from 1 to 9999 = 9999 numbers Find number that do NOT contain digit 5.
We subtract that from 9999. Digits allowed (excluding 5): 0,1,2,3,4,6,7,8,9 → 9 digits Count numbers that do not have digit 5: 1-digit: 8 (1–9 except 5) 2-digit: 8 × 9 = 72 3-digit: 8 × 9 × 9 = 648 4-digit: 8 × 9 × 9 × 9 = 5832 Total = 8 + 72 + 648 + 5832 = 6560
So numbers with digit 5 at least once = 9999 - 6560 = 3439
We subtract that from 9999. Digits allowed (excluding 5): 0,1,2,3,4,6,7,8,9 → 9 digits Count numbers that do not have digit 5: 1-digit: 8 (1–9 except 5) 2-digit: 8 × 9 = 72 3-digit: 8 × 9 × 9 = 648 4-digit: 8 × 9 × 9 × 9 = 5832 Total = 8 + 72 + 648 + 5832 = 6560
So numbers with digit 5 at least once = 9999 - 6560 = 3439
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