The number of natural numbers less than $10000$ which are divisible by $5$ and in which no digit is repeated is:

The number of positive integral solutions of $abc = 30$ is

$^n{P_r} \div ^n{C_r} = $

The number of permutations of the digits $1, 2, 3, ..., 7$ without repetition,which neither contain the string $153$ nor the string $2467$,is $........$.

If the number of seven-digit numbers,such that the sum of their digits is even,is $m \cdot n \cdot 10^{n}$; $m, n \in \{1, 2, 3, \ldots, 9\}$,then $m+n$ is equal to . . . . . . .

Let $n$ be the number of ways in which $5$ boys and $5$ girls can stand in a queue such that all the girls stand consecutively. Let $m$ be the number of ways in which $5$ boys and $5$ girls can stand in a queue such that exactly four girls stand consecutively. Then the value of $\frac{m}{n}$ is