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

The number of ways in which $3$ boys and $4$ girls can be seated around a circular table if no two boys sit together is

$A$ round table conference is to be held amongst $20$ countries. If two particular delegates wish to sit together,then in how many ways can such arrangements be done?

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

Find the number of different garlands that can be prepared using $5$ different coloured flowers.

In how many ways can $5$ men and $2$ women be seated around a circular table such that the two women do not sit together?