Question

Find the chance that last digit of the product is $A_5$

• A. $\frac{6^n-5^n}{{10}^n}$
• B. $\frac{5^n-4^n}{{10}^n}$
• C. $\frac{6^n-4^n}{5^n}$
• D. $\frac{4^n-2^n}{5^n}$

Answer 1

The correct option is B $\frac{5^n-4^n}{{10}^n}$

Now $A_5=$ The last digit of the product is the number
5. Iflast digit in the product is 5, one of the number must end in 5 & all the rest must be odd. Now there are 5 odd digits in all & hence $5^n$ is the number of ways in which odd digit can be chosen to end the number in the odd digit so 4" are the cases in which odd digit can be selected only from 1,3,7 or 9
$\therefore n\left(A_5\right)=5^n-4^n$
$\therefore P\left(A_5\right)=\frac{5^n-4^n}{{10}^n}$