Answer :
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
.
.
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Variable number With 7 character = [tex]53 \times 63^{7}[/tex]
Total difference variable = 53 + 53 × 63+ 53 × 63²+ 53 × 63³+....+ [tex]63^{7}[/tex]
Total difference variable = 53(1 + 63 + 63²+ 63³+ .... + [tex]63^{7}[/tex])
Formula:
[tex]1+x+x^2+x^3+x^4+........x^n\\\\\Rightarrow \frac{x^{(n+1)} -1}{x-1}[/tex]
Total difference variable
[tex]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[/tex]