The number of times the digit 5 will be written when listing the integers from 1 to 1000 , is

Step-by-step solution

Any number between 1 to 999 is of the form a b c when 0 ≤ a , b , c ≤ 9 . Let us first count the number in which 5 occurs exactly once. Since, 5 can occur at one place in 1 × C 1 3 × 9 × 9 = 243 ways, next 5 can occur in exactly two places in C 2 3 × 9 = 27 . Lastly, 5 can occur in all three digits in only one way. Hence, the number of times 5 occurs = 1 × 243 + 27 × 2 + 1 × 3 = 243 + 54 + 3 = 300