Assignment:
The name of a variable in the C programming language is a string that can contain uppercase letters, lowercase letters, digits, or underscores. Further, the first character in the string must be a letter, either uppercase or lowercase, or an underscore. If the name of a variable is determined by its first eight characters, how many different variables can be named in C? Note that the name of a variable may contain fewer than eight characters.
Provide complete and step by step solution for the question and show calculations and use formulas.