If $\frac{1}{8!} + \frac{1}{9!} = \frac{x}{10!},$ find $x.$

The total number of integral solutions of the equation $xyz = 24$ is

The total number of $3$-digit numbers,whose greatest common divisor with $36$ is $2$,is

Five balls of different colours are to be placed in three boxes of different sizes. The number of ways in which we can place the balls in the boxes so that no box remains empty is

The number of positive integral solutions of $xyz = 60$ is

Numbers are to be formed between $1000$ and $3000$,which are divisible by $4$,using the digits $1, 2, 3, 4, 5$ and $6$ without repetition of digits. Then the total number of such numbers is.