If the number of five-digit numbers with distinct digits and $2$ at the $10^{\text{th}}$ place is $336k$,then $k$ is equal to

All the letters of the word '$EAMCET$' are arranged in all possible ways. The number of such arrangements in which two vowels are not adjacent to each other is

$A$ parallelogram is cut by two sets of $m$ lines parallel to its sides. The number of parallelograms thus formed is

In a circus, there are $10$ cages to accommodate $10$ animals. Out of these, $4$ cages are so small that $5$ specific animals cannot enter them. In how many ways is it possible to accommodate the $10$ animals in these $10$ cages?

The number of ways in which we can select three numbers from $1$ to $30$ so as to exclude every selection of all even numbers is

The number of times the digit $3$ will be written when listing the integers from $1$ to $1000$ is