How many license plates with 3 decimal digits followed by 3 letters do not contain both the number 0 and the letter O?
I tried by working like since 0 is not allowed and the letter 'O' is not allowed so possible number of license plates=$9*9*9*25*25*25$ but this is not the answer.
When I checked the solution, it was like total 3 decimal digits, which contain $0$ is $10^3-9^3$ And total letters which contain $O$ is $26^3-25^3$ Hence required number of license plates=$10^3.26^3-(10^3-9^3) \times(26^3-25^3).$
I want to know where my approach failed. I understood the solution, but unless I understand where I failed, getting the solution is of no use.
Please help.
Your approach is missing the cases where either O or 0 can be in the licence plate. For Eg, 045FTD can be licence plate number but your approach will miss these kind of licence numbers.