If 5 positive integers are taken at random and multiplied together. The probability that the last digit of the product is 2, 4, 6, 8 is

5 Positive integers are taken at random and multiplied together

$\mathrm{n}\left(\mathrm{S}\right)={10}^5$

E=last digit of the product is 2, 4, 6, 8

$\begin{array}{rcl}\mathrm{n}\left(\mathrm{E}\right)& =& 8^5-4^5\\ \mathrm{P}\left(\mathrm{E}\right)& =& \frac{8^5-4^5}{{10}^5}=\frac{4^5-2^5}{5^5}\end{array}$