In how many ways can $12$ gentlemen sit around a round table so that three specified gentlemen are always together?

If $^{43}C_{r-6} = ^{43}C_{3r+1}$,then the value of $r$ is

The number of ways of dividing $52$ cards amongst four players so that three players have $17$ cards each and the fourth player has just one card,is

There are $6$ Men and $8$ Women in a club in which a committee of $5$ people has to be made. What will be the number of ways to select $5$ people if at most one man is selected?

The sum of the digits in the unit's place of all the $4-$digit numbers formed by using the digits $3, 4, 5,$ and $6$,without repetition,is

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