The code of a student is a sequence consisting of 6 characters, each of which is either one of the 26 letters of the English alphabet or one of the digits 0,1,.......,9. How many codes are there which contain at most two digits?
I did it in this way, but i am not quite sure in my result.
We have 10 choises for choosing numbers and 26 for letters. Our code should contain at most 2 digits, so we have 4 letters left. Order matters, therefore we should handle this problem with help of permutations. Thus, (10 * 9) * (26 * 25 * 24 * 21) , where (10 * 9) is choises for choosing any number between 0 - 9 and (26 * 25 * 24 * 21) for choosing 4 letters among 26. Is this solution correct or i misunderstood something?
Thanks in advance.