Question

The number of times the digit 3 will be written when listing the integers from 1 to 1000 is

• A. 269
• B. 300
• C. 271
• D. 302

Answer 1

Answer: (B)

300

Answer 2

To find the number of times 3 occurs in listing the integer from 1 to 999. (since 3 does not occur in 1000). Any number between 1 to 999 is a 3 digit number xyz where the digit x, y, z are any digits from 0 to 9.

Now, we first count the numbers in which 3 occurs once only, Since 3 can occur at one place in ³C₁ ways, there are ³C₁.

(9 x 9) = 3.9² such numbers.

Again, 3 can occur in exactly two places in ³C₁(9) such numbers. Lastly 3 can occur in all the three digits in one such number only 3337.

∴ The number of times 3 occurs is equal to

1 x (3 x 9²) + 2 x (3 x 9) + 3 x 1 = 300.