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

Options

A. 269
B. 271
C. 300
D. 302

Answer

C

Explanation

Since, 3 does not occur inn 1000. so, we have to count the number of times 3 occurs, when we list the integers from 1 to 999.
Any number of between 1 and 999 is of the form xyz, where `0 le x , y, z le9`.
Let us first count the number in which 3 occurs exactly once. since, 3 can occur at one place inn `.^(3)C_(1)` ways, there are `.^(3)C_(1)xx9xx9=243` such numbers. next 3 can occur in exactly two places in `.^(3)C_(2)xx9=27` such numbers. lastly, 3 can occur in all three digits in one number only. hence, the number of times, 3 occcurs is `1xx243+2xx27+3xx1=300`