$6$ 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 $p/q =$

In how many ways can four children be made to stand in a line such that two of them,$A$ and $B$,are always together?

Everybody in a room shakes hands with everybody else. The total number of handshakes is $66$. The total number of persons in the room is:

The number of ways in which any four letters can be selected from the word $CORGOO$ is

The number of ways in which an examiner can assign $30$ marks to $8$ questions,awarding not less than $2$ marks to any question is

At an election,a voter may vote for any number of candidates,not greater than the number to be elected. There are $10$ candidates and $4$ are to be selected. If a voter votes for at least one candidate,then the number of ways in which he can vote is