In how many ways can $5$ keys be put in a ring?

The number of ways in which $5$ boys and $4$ girls can sit around a circular table such that no two girls sit together is:

If $3$ sisters and $8$ other girls are together playing a game,then the number of ways in which all the girls are seated around a circle such that the three sisters are not seated together,is

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:

If a party of $n$ persons sit at a round table,then the odds against two specified individuals sitting next to each other are

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