Answer: Option B
:
B
To find the number of times 3 occurs in listing the integer from 1 to 999. (since 3 does notoccur in 1000). Any number between 1 to 999 is a 3 digit number xyzz 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 ${}^3{C}_1.(9\times 9)$ = ${3.9}^2$such numbers.
Again, 3 can occur in exactly two places in ${}^3{C}_1\left(9\right)$ such numbers. Lastly 3 can occur in all the three digits in one such number only 333.
$\therefore$The number of times 3 occurs is equal to $1\times (3\times 9^2)+2\times (3\times 9)+3\times 1$=300.