Quote:
Mr Bob wrote the counting in his notebook from 1 to 100000. How many times he has written the digit ‘8' while writing the integers from 1 to 100000?
A. 15000
B. 18000
C. 25000
D. 50000
E. 55000
consider the following cases:
single digit: one time 8 will be written: 1
two digits:
case 1: unit digit is 8, other digits can be filled in 9 ways: 9; numbers will be from 1-9
case 2: ten digit is 8, other digits can be filled in 10 ways: 10
total = 19
three digits:
case 1: unit digit is 8, other digits can be filled in 9*10 ways: 90
case 2: tens digit is 8, other digits can be filled in 9*10 ways: 90
case 3: hundreds digit is 8, other digits can be filled in 10*10 ways: 100
total = 280
four digits:
case 1: unit digit is 8, other digits can be filled in 9*10*10 = 900
case 2: tens digit is 8, other digits can be filled in 9*10*10 = 900
case 3: hundreds digit is 8, other digits can be filled in 9*10*10 = 900
case 4: thousands digit is 8, other digits can be filled in 10*10*10 = 1000
total = 3700
five digits:
case 1: unit digit is 8, other digits can be filled in 9*10*10*10 = 9000
case 2: tens digit is 8, other digits can be filled in 9*10*10*10 = 9000
case 3: hundreds digit is 8, other digits can be filled in 9*10*10*10 = 9000
case 4: thousands digit is 8, other digits can be filled in 9*10*10*10 = 9000
case 5: ten thousands digit is 8, other digits can be filled in 10*10*10*10 = 10000
total = 46000 + 3700 + 280 + 19 + 1 = 50000
Ans: D