possible number of PAN card numbers Permanent Account Number (PAN) is a code that acts as identification of Indians. An example number would be in the form of AAAPL1234C. The format is 


*

*The first three letters are sequence of alphabets from AAA to ZZZ

*The fourth character informs about the type of holder of the card (possible letters A, B, C, F, G, H, L, J, P, T, K)

*The fifth character of the PAN is the first character


*

*of the surname or last name of the person, in the case of a "Personal" PAN card

*of the name of the Entity, Trust, society, or organisation in the case of Company/ HUF/ Firm/ AOP/ BOI/ Local Authority/ Artificial Judicial Person/ Govt


*next four numbers are ranging from 0001 to 9999

*The last character is an alphabetic check digit


reference: wiki
Now, I'm trying to find the total possible number of PAN numbers like below


*

*for first 3 alphabets - 26 * 26 * 26

*fourth letter have only 11 possiblities - 11

*fifth letter can be any of the 26 alphabets - 26

*next 4 letters are between 0001 to 9999 - 9999

*last letter can be any of the 26 aplhabets - 26


so total would be 26 * 26 * 26 * 11 * 26 * 9999 * 26.
is this correct or am I missing something? 
 A: If everything you say is true, then yes you are correct. I just have concerns about items 4. and 5.


*You are correct if these four numbers are any numbers $0001$ to $9999$. There are $9999$ possible numbers. However, it is possible that the first three digits are any value $0$ to $9$ and the last digit is any value $1$ to $9$. In this case there are $10\times10\times10\times9 = 9000$ ways to fill out these four digits. This case excludes all values that end in $0$, like $10, 100, 1000$, etc.

*It is possible that there is some algorithm to calculate this "alphabetic check", so it might not be true that all 26 letters are possible.
I do not believe the article addressed these two items. If we simply ignore them and assume that your understanding of the structure is correct, then your calculation is correct.  
A: Correct answer is $26 \cdot 26 \cdot 26 \cdot 11 \cdot 26 \cdot 9999$ because last digit is not controllable and for precious 9 digit you will not find different value of 10th digit for same 9 digit
