The number of words which can be formed from the letters of the word $MAXIMUM$,if two consonants cannot occur together,is

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

If the letters of the word $SACHIN$ are arranged in all possible ways and these words are written out as in a dictionary,then the word $SACHIN$ appears at serial number:

$5$-digit numbers are to be formed using $2, 3, 5, 7, 9$ without repeating the digits. If $p$ is the number of such numbers that exceed $20000$ and $q$ is the number of those that lie between $30000$ and $90000$,then $p : q$ is

The number of numbers that can be formed with the help of the digits $1, 2, 3, 4, 3, 2, 1$ so that odd digits always occupy odd places,is

The range of the function $f(x) = {}^{7 - x}P_{x - 3}$ is