Question

If the four positive integers are selected randomly from the set of positive integers, then the probability that the number $1,3,7$ and $9$ are in the unit place in the product of $4-$digit, so selected is

• A. $\frac{7}{625}$
• B. $\frac{2}{5}$
• C. $\frac{5}{625}$
• D. $\frac{16}{625}$

Answer 1

The correct option is D $\frac{16}{625}$

The number of digits on unit place of any number $=10$

$\therefore n\left(S\right)=10$

The necessary condition for becoming the digits $1,3,5$ or $7$ at the unit place of product of four numbers that the digits $1,3,5$ or $7$ at unit place of every number.
$\therefore n\left(A\right)=4$

$\therefore P\left(A\right)=\frac{4}{10}=\frac{2}{5}$

So, required probability $={\left(\frac{2}{5}\right)}^4=\frac{16}{625}$