Question
Question: The number of times the digit 3 will be written when listing the integers from 1 to 1000 is-...
The number of times the digit 3 will be written when listing the integers from 1 to 1000 is-
A
269
B
300
C
271
D
302
Answer
300
Explanation
Solution
Treat all numbers from 1 to 1000 as three digit number for example 3 = 003, 32 = 032, 125 = 125 etc. Then by principle of homogeneity 3 will appear at each place in 100 ways (since there are 1000 numbers and each number from 0 to 9 is equally likely). Thus total number of times 3 will be written = 100 × 3 = 300.