Assignment:
Q1. A telephone number is a ten-digit number whose first digit cannot be a 0 or a 1. How many telephone numbers are possible?
Q2. 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 in the file name is at most eight (and there has to be at least one character in the file name). For example, X23, W, 4AA and ABCD1234 are valid file names, but W-23 and WONDERFUL are not valid (the first has an improper character, the second is too long). How many different file names are possible in this system?
Q3. A class contains ten boys and ten girls. In how many different ways can they stand in a line if they must alternate in gender (no two boys and no two girls are standing next to eachother)?
Provide complete and step by step solution for the question and show calculations and use formulas.