The number of ways in which $8$ different pearls can be arranged to form a necklace is

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

$A$ 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?

If $11$ members of a committee sit at a round table so that the President and Secretary always sit together,then the number of arrangements is

The number of ways in which $6$ men and $5$ women can sit at a round table,if no two women sit together,is:

If $5$ red roses and $5$ white roses of different sizes are used in preparing a garland,the probability that red and white roses come alternately is