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

Answer:

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  = $53 \times 63^{7}$

Total difference variable = 53 + 53 × 63+ 53 × 63²+ 53 × 63³+....+ $63^{7}$

Total difference variable = 53(1 + 63 + 63²+ 63³+ .... + $63^{7}$)

Formula:

$1+x+x^2+x^3+x^4+........x^n\\\\\Rightarrow \frac{x^{(n+1)} -1}{x-1}$

Total difference variable

$53 \times \frac{63^{7+1} -1 }{63-1}\\\\53 \times \frac{63^{8} -1 }{63-1} \\\\ \therefore 63^8 = 2.48 \times 10^{14}\\\\53 \times \frac{2.48 \times 10^{14} -1 }{62}\\\\53 \times \frac{1.48 \times 10^{14}}{62}\\\\21213316700$