Question

(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

Answer 1

The different variable in C is 21213316700.

Step-by-step 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 =
`53 * 63^(7)`

Total difference variable = 53 + 53 × 63+ 53 × 63²+ 53 × 63³+....+
`63^(7)`

Total difference variable = 53(1 + 63 + 63²+ 63³+ .... +
`63^(7)`)

Formula:

`1+x+x^2+x^3+x^4+........x^n\\\\\Rightarrow (x^((n+1)) -1)/(x-1)`

Total difference variable

`53 * (63^(7+1) -1 )/(63-1)\\\\53 * (63^(8) -1 )/(63-1) \\\\ \therefore 63^8 = 2.48 * 10^(14)\\\\53 * (2.48 * 10^(14) -1 )/(62)\\\\53 * (1.48 * 10^(14))/(62)\\\\21213316700`