Num of 1 letter code = 26
Num of 2 letter code = 26 * 26 ( as letters can be repeated )
Num of 3 letter code = 26 * 26 * 26 ( as letters can be repeated )

So, total num of codes that can be formed = 26 + 26^2 + 26^ 3
= 18278 = Ans E

Please let me know the OA