Discrete math problems
1. A telephone number is a ten-digit number whose first
digit cannot be a 0 or a 1. How many telephone numbers are possible?
2. 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?
3. 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)?
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