In how many ways can the letters of the word $EAMCET$ be arranged such that no two vowels are together?

Find the number of different $8$-letter arrangements that can be made from the letters of the word $DAUGHTER$ such that all vowels occur together.

$6$ boys and $5$ girls sit in a line such that $(I)$ no two girls sit together $(II)$ all the girls sit together. If $p$ is the number of arrangements in case $(I)$ and $q$ is the number of arrangements in case $(II)$,then $p/q =$

In a train,five seats are vacant. In how many ways can three passengers sit?

Ten persons,amongst whom are $A, B$ and $C$,are to speak at a function. The number of ways in which it can be done if $A$ wants to speak before $B$ and $B$ wants to speak before $C$ is:

There are $9$ balls to be placed in $9$ boxes. If $5$ of the balls cannot fit into $3$ specific small boxes,find the number of ways to arrange exactly one ball in each of the boxes.