$A$ couple can sit with $6$ guests around a circular table. In how many ways can they sit if the couple sits in consecutive seats?

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 that $8$ beads of different colours can be strung as a necklace is

The number of ways in which $6$ boys and $4$ girls can be seated around a round table such that $2$ special boys and a special girl never sit together is

In how many ways can $7$ men and $7$ women be seated around a circular table such that no two women sit together?

The number of ways of arranging $2$ red,$3$ white,and $5$ yellow roses of different sizes into a garland such that no two yellow roses come together is