5. (11 points) In a version of the BASIC programming language, the name of a variable is a string of 1 or 2 alphanumeric characters, where uppercase and lowercase letters are not distinguished. Moreover, a variable name must begin with a letter and must be different from the five strings of two characters that are reserved for programming use. How many different variables names are there?
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Since uppercase and lowercase letters are not distinguished, we have 26 possibilities for the first character. For the second character, we can have either a letter or a number, so we have 26 possibilities for a letter and 10 possibilities for a number, giving Show more…
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A common computer programming rule is that names of variables must be between one and eight characters long. The first character can be any of the 26 letters, while successive characters can be any of the 26 letters or any of the 10 digits. For example, allowable variable names include A, BBB, and M3477K. How many different variable names are possible? (Ignore the difference between uppercase and lowercase letters.)
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