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 3 C 1 ways, there are 3 C 1 . (9 x 9) = 3.9 2 such numbers.

Again, 3 can occur in exactly two places in 3 C 1 (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 9 2 ) + 2 x (3 x 9) + 3 x 1 = 300.