I am not sure I understand completely what you are looking for but your answer gives me a clue. You use the word combinations which to me says that order doesn't matter. That is a1 and 1a are the same combination. I don't think that this is what you mean since that would mean that 35 and 53 are the same combination. Also you didn't write the digit 0 anywhere but you have 1 as a two character combination so I assume you are identifying 1 and 01. If 0 is an allowable symbol then you have 26 letters and 10 digits for a total of 36 characters. The clue in your answer come from the fact that
362 = 1296. So let me reword the question.
How many two character "words" can I form using an "alphabet" composed of the 26 letters in the english alphabet and the 10 digits 0 to 9?
Think about writing such a "word". For the first "letter" you can choose any one of the 36 allowable characters. Then, after writing the first character you have a choice of any of the 36 allowable characters for the second "letter". Thus you can construct the "word" in 36 36 = 1296 ways.
Did you count 00 as an allowable "word"?