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## Homework Statement

A computer operating system allows files to be named using any combination of uppercase letters (A-Z) and digits (0-9) But the number of characters is at most 4 , And there must be at least 1 letter in each file name.

## The Attempt at a Solution

So I break this up into 4 cases. 1 character file name , 2 character file name , 3 character file name , 4 character file name.

For the first case I just have 26 choices because it has to be a letter.

and for the second one I have 2 characters, To make sure I have at least one letter in it

I take all the possible combinations 36*36 minus the combinations with no letters

so I should have [itex] 36^2-10^2 [/itex] for the second one. And this pattern should continue.

So i think the answer is [itex] (26)+(36^2-10^2)+(36^3-10^3)+(36^4-10^4) [/itex]

I didn't simply this so you can see my reasoning.