A shelf contains 20 books of which 4 are single volume and the other form sets of 8, 5, and 3 volumes. Find the number of ways in which the books may be arranged on the shelf so that
volumes of each set will not be separated,

A bag contains 5 blue and 6 white balls. Determine the number of ways in which 3 blue and 4 white balls can be selected.

There are 20 persons, among whom two are brothers. Find the number of ways in which we can arrange the 20 persons around a round table so that there is exactly one person between the two brothers.

A bag contains 5 white, 6 red and 4 blue balls. Determine the number of ways in which 2 white, 3 red and 2 blue balls can be selected.

Eight identical spheres of radius R are arranged in contact with each other to form a cubic pattern and is placed inside a cubic container of size just enough to contain them. What fraction of the volume of the container does the spheres occupy