How many words,with or without meaning,can be formed from the letters of the word $MONDAY$,assuming that no letter is repeated,if all letters are used at a time?

The number of ways in which $5$ boys and $3$ girls can be seated in a row so that each girl is between two boys.

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

If $a$ denotes the number of permutations of $x + 2$ things taken all at a time,$b$ the number of permutations of $x$ things taken $11$ at a time,and $c$ the number of permutations of $x - 11$ things taken all at a time such that $a = 182bc$,then the value of $x$ is

For $1 \leq r \leq n$,the value of $\frac{1}{r+1}\left\{{ }^n P_{r+1}-{ }^{(n-1)} P_{r+1}\right\}$ is equal to

The number of numbers,strictly between $5000$ and $10000$,that can be formed using the digits $1, 3, 5, 7, 9$ without repetition is $..........$.