what do u mean by 2 algarisms diferents?
please give me at least an example, so I will try to solve it for u.
Also, credit card with sixteen zeros is it countable?
It's not clear what you are asking.
In your example 1122 & 1112, are you looking for the manner in which the check digit is determined?
Each credit card company has it's own algorithm for it's credit card number.
I'm guessing that your word "algarism" means the same as "algorithm"
Need a little more information, a more detailed example.
Can you supply some additional data?
Apparently, "algarism" is an arcane word for "digit", or "numeral". See, e.g., this Yahoo question or this article (written in English by Brazilians) that contains the following phrase: "The deviation on the fifth decimal algarism can be attributed to the accuracy of the numerical calculation." In fact, "algarismo" means "digit" in Portuguese.
Well you need to choose two digits, so that can be done in 9*10 ways. Now you have 3 different cases. First digit goes in the code once, second twice; both of them go in the code twice; first goes three times.
You need to permute the digits for all of the three cases so in the end you have
9*10*(4!/3! + 4!/(2!*2!) + 4!/3!)