How many $5$-digit numbers can be formed without any conditions?

Words of length $10$ are formed using the letters $A, B, C, D, E, F, G, H, I, J$. Let $x$ be the number of such words where no letter is repeated,and let $y$ be the number of such words where exactly one letter is repeated twice and no other letter is repeated. Then,$\frac{y}{9x} =$

How many $8$-digit numbers can be formed such that all digits are distinct?

In how many ways can $mn$ letters be posted in $n$ letter-boxes?

The number of ways to seat $3$ men and $2$ women in a bus such that the total number of seated men and women on each side is $3$ is:

$4$ buses run between Bhopal and Gwalior. If a man goes from Gwalior to Bhopal by a bus and comes back to Gwalior by a different bus,then the total number of possible ways is: