TITLE: How many possible combinations of a HEX string
QUESTION [6 upvotes]: I am trying to figure out the maximum possible combinations of a (HEX) string, with the following rules:

All characters in uppercase hex (ABCDEF0123456789)
The output string must be exactly 10 characters long
The string must contain at least 1 letter
The string must contain at least 1 number
A number or letter can not be represented more than 2 times

I am thinking the easy way to go here (I am most likely wrong, so feel free to correct me):

Total possible combinations:  $16^{10} = 1,099,511,627,776$
Minus all combinations with just numbers: $10^{10} = 10,000,000,000$
Minus all combinations with just letters: $6^{10} = 60,466,176$
etc...

Can someone could tell me if this is the right way to go and if so, how to get the total amount of possible combinations where a letter or a number occur more than twice.
Any input or help would be highly appreciated!
Muchos thanks!
PS.
I don't know if I tagged this question right, sorry :(
DS.

REPLY [2 votes]: Four years and no answer?  To continue with your original reasoning...
Total amount of numbers: $10^{10}$ or 10,000,000,000
Total amount of letters: $6^{10}$ or $60,466,176$
Subtract the above two numbers $10^{10}$ and $6^{10}$ from...(drum roll please)...Your last criteria! ("A number or letter cannot be represented more than $2$ times").
So your final answer is: $264,683,239,424$.
I'm sure you're wondering what the probability of your last criteria is.  It would be: ($16^2)*(15^2)*(14^2)*(13^2)*(12^2)$.
That is, every two numbers I reduce by one, because for every two spaces, one number cannot repeat.  Thanks.