How many words,with or without meaning,can be formed using all the letters of the word $EQUATION$ at a time so that the vowels and consonants occur together?

If the best and the worst paper never appear together,then in how many ways can $6$ examination papers be arranged?

Using the digits $0, 2, 4, 6, 8$ not more than once in any number,the number of $5$-digit numbers that can be formed is:

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

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

The number of distinct positive integers that can be formed using $0, 1, 2, 3$,where each integer is used at most once,is equal to