(5 pt.) The name of a variable in the C programming language is a string that can contain uppercase letters, lowercase letters, digits, or underscores. Furthermore, 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 8 characters, how many different variables can be named in C

The different variable in C is 21213316700.

Explanation:

Given value:

Total value  = letters + underscore value

Total value  = 52 + 1

Total value =53

choice for first character = 53 letters +10 digits

first character = 63

choice for remaining characters

So,

Variable number With one 1 character = 53

Variable number With 2 character  = 53 × 63

Variable number With 3 character = 53 × 63²

Variable number With 4 character  = 53 × 63³

.

.

.

Variable number With 7 character  =

Total difference variable = 53 + 53 × 63+ 53 × 63²+ 53 × 63³+....+

Total difference variable = 53(1 + 63 + 63²+ 63³+ .... + )

Formula:

Total difference variable