UPSC Prelims 2006·GS1·science-and-technology·science and technology

How many numbers are there in all 6000 to 6999 (Both 6000 and 6999 included) having at least one of their digits repeated?

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Last updated 8 Jul 2026, 4:39 pm IST
  1. A216
  2. B356
  3. C496Correct
  4. D504

Explanation

To find the number of values between 6000 and 6999 where at least one digit is repeated, it is easiest to subtract the numbers with no repeated digits from the total count.

Step 1: Calculate the total numbers in the range. From 6000 to 6999, there are exactly 1000 numbers.

Step 2: Calculate how many numbers have no repeated digits. All numbers in this range start with the digit 6. To have no repetitions, the remaining three positions must be filled using the remaining nine digits (0, 1, 2, 3, 4, 5, 7, 8, 9). The second digit can be any of the 9 available digits. The third digit can be any of the remaining 8 digits. The fourth digit can be any of the remaining 7 digits. Calculation: 1 multiplied by 9 multiplied by 8 multiplied by 7 equals 504.

Step 3: Subtract the non-repeated count from the total count. 1000 minus 504 equals 496.

Therefore, there are 496 numbers that have at least one digit repeated. The correct option is C.

science-and-technology: How many numbers are there in all 6000 to 6999 (Both 6000 and 6999 included) having at least one of their digits repeate
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