$10$ men and $6$ women are to be seated in a row so that no two women sit together. The number of ways they can be seated is:

$6$ boys and $5$ girls sit in a line such that $(I)$ no two girls sit together $(II)$ all the girls sit together. If $p$ is the number of arrangements in case $(I)$ and $q$ is the number of arrangements in case $(II)$,then $p/q =$

The number of words,which can be formed using all the letters of the word $\text{DAUGHTER}$,so that all the vowels never come together,is

Find the number of arrangements of the letters of the word $INDEPENDENCE$. In how many of these arrangements do all the vowels always occur together?

The digits $4, 5, 6, 7, 8$ are written in every possible order. The number of numbers greater than $56000$ is

The letters of the word $OUGHT$ are written in all possible ways and these words are arranged as in a dictionary,in a series. Then the serial number of the word $TOUGH$ is :