How many words can be formed using the letters of the word $SCHOLAR$ that start with $A$ and end with $S$?

Find the number of $4$ letter words,with or without meaning,which can be formed out of the letters of the word $ROSE$,where the repetition of the letters is not allowed.

How many ways are there to arrange the letters of the word $EDUCATION$ so that all the following three conditions hold?
- The vowels occur in the same order $(E, U, A, I, O)$.
- The consonants occur in the same order $(D, C, T, N)$.
- No two consonants are next to each other.

How many words can be formed using the letters of the word $ALLAHABAD$?

Three children,each accompanied by a guardian,seek admission in a school. The principal wants to interview all the $6$ persons one after the other subject to the condition that no child is interviewed before its guardian. In how many ways can this be done?

$A$ vehicle registration number consists of $2$ letters of the English alphabet followed by $4$ digits, where the first digit is not zero. The total number of vehicles with distinct registration numbers is