How many numbers between $5000$ and $10000$ can be formed using the digits $1, 2, 3, 4, 5, 6, 7, 8, 9$ if no digit is repeated?

The number of different permutations that can be formed by taking $4$ letters at a time from the letters of the word '$REPETITION$' is

How many arrangements of $3$ letters can be made from the letters $a, b, c, d, e, f$ without repetition,such that each arrangement contains at least one vowel?

How many numbers greater than $100$ and divisible by $5$ can be made from the digits $3, 4, 5, 6$,if no digit is repeated?

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.

All the letters of the word $GTWENTY$ are written in all possible ways with or without meaning and these words are written as in a dictionary. The serial number of the word $GTWENTY$ is: