Complete the following proof that there cannot be a perfect data compression program, i.e. a program that will reduce the length of any file it encounters. Suppose we had such a program. It follows that when we apply this program to an input file of bit length n, it produces an output file of bit length at most n - 1. There are 2^n possible input files of length n, and at most 2^n - 1 output files of length at most n - 1. A site requires you to pick a password that has exactly 10 letters (upper or lower case English alphabet) and 3 digits. The numbers and letters can be mixed and do not need to grouped with each other. How many possible passwords are there? Give the exact answer, but do not evaluate