Explanation

(b)
Any number between 1 to 999 is a 3 digit number $xy\mathcal{z}$ where the digits $x,y,\mathcal{z}$ are any digits from 0 to 9.
Now, we first count the number 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 occur in exactly two places in $\ ^{3}C_{2}.(9)$ such numbers. Lastly 3 can occur in all the three digits in one such number only 333
$\therefore$ The number of times 3 occurs
$= 1 \times \left( 3 \times 9^{2} \right) + 2 \times (3 \times 9) + 3 \times 1 = 300$