The number of ways in which $5$ male and $2$ female members of a committee can be seated around a round table so that the two female members are not seated together is:

The number of circular permutations of $n$ distinct objects is......

The number of ways of arranging all the letters of the word "$COMBINATIONS$" around a circle so that no two vowels come together is

Find the number of ways in which two Americans,two British,one Chinese,one Dutch,and one Egyptian can sit at a round table so that persons of the same nationality are separated.

$A$ family consisting of a mother,father,and their $8$ children ($4$ boys and $4$ girls) are to be seated at a round table in a party. How many ways can this be done if the mother and father sit together and the males and females alternate?

The number of ways in which $5$ boys and $3$ girls can be seated on a round table,if a particular boy $B_1$ and a particular girl $G_1$ never sit adjacent to each other,is