The name of a variable in the X programming language is a string of at least one and at most eight characters that can contain uppercase letters, lowercase letters, digits, or underscores. The first character in a variable name must be a letter, either uppercase or lowercase. How many different variable names can a program in the X programming language use?

204,826,993,236,684 possible variables

Explanation:

Upper case characters = 26

Lower case = 26

Digit = 10

Underscore = 1

Total Characters = 26 + 26 + 10 + 1 = 63

The following is the possible string selection of string of 8 characters that follow the above rule

First character = Upper case or Lower case = 26 + 26 = 52

Since there's no restriction on repitition of characters,

The second, third, fourth, fifth, sixth, seventh and eighth character could be any character

Second character = 63

Third character = 63

Fourth = 63

Firth = 63

Sixth = 63

Seventh = 63

Eight = 63

Total number of characters = 52 * 63 * 63 * 63 * 63 * 63 * 63 * 63

Total = 52 * 63^7

Total = 204,826,993,236,684 possible variables