The number of all four-digit numbers which begin with $4$ and end with either $0$ or $5$ is:

How many numbers greater than $24000$ can be formed using the digits $1, 2, 3, 4, 5$ without repetition?

How many words of $4$ distinct letters can be formed using the letters of the word $DHOLPUR$ if $L$ and $P$ are always excluded?

In how many ways can the letters of the word $PERMUTATIONS$ be arranged if the vowels are all together?

There are $15$ stations on a railway line. How many different types of tickets must be printed so that a passenger can travel from any station to any other station?

Ten chairs are numbered as $1$ to $10$. Three women and two men wish to occupy one chair each. First,the women choose the chairs marked $1$ to $6$,then the men choose the chairs from the remaining. The number of possible ways is