If $^n{P_5} = 9 \times {^{n - 1}}{P_4}$,then the value of $n$ is

In how many ways can the letters of the word $MAXIMA$ be arranged such that all vowels are together and all consonants are together?

If all possible numbers are formed by using the digits $1, 2, 3, 5, 7$ without repetition and they are arranged in descending order,then the rank of the number $327$ is

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.

Eight chairs are numbered $1$ to $8$. Two women and three men wish to occupy one chair each. First,the women choose chairs from amongst the chairs marked $1$ to $4$,and then the men select the chairs from amongst the remaining. The number of possible arrangements is

Four speakers will address a meeting where speaker $Q$ will always speak before $P$. Then, the number of ways in which the order of speakers can be prepared is