The name of a variable in the JAVA programming language is a string of $1$ to $65,535$ characters, where each character can be an uppercase or a lowercase letter, a dollar sign, an underscore, or a digit. Furthermore, the first character in the string must not be a digit. How many different variable names are there in JAVA?
I know there are the following characters:
- $26$ Lowercase Letters
- $26$ Uppercase Letters
- $1$ Dollar Sign ($) - $1$ Underscore(_)
For a total of $54$ ways.
I am unsure where to go from this point. If this could be worked out with an explanation it would be much appreciated.
Hint: Do you recognize the exponent on $r$ as the number of characters after the first? How many one character names are there? What does that represent?