Question

The chance that last digit of the product is$A_7$ is?

• A. $\frac{8^n+5^n-4^n}{{10}^n}$
• B. $\frac{8^n-5^n-4^n}{{10}^n}$
• C. $\frac{{10}^n-8^n-5^n+4^n}{{10}^n}$
• D. None of these

Answer 1

The correct option is A $\frac{8^n+5^n-4^n}{{10}^n}$

$A_7=$ The last digit is 1,2,3,4,5,6,7,8 or 9 $=\{1,3,7,9\}\cup \{2,4,6,8\}\cup \left\{5\right\}$
$\therefore n\left(A_7\right)=n\left(A_3\right)+n\left(A_4\right)+n\left(A_5\right)$
$\therefore 4^n+8^n-4^n+5^n-4^n=8^n+5^n-4^n$
$\therefore P\left(A_7\right)=\frac{n\left(A_7\right)}{n\left(S\right)}=\frac{8^n+5^n-4^n}{{10}^n}$ Choice (a) is correct.