Final answer:
The caste not part of the Azawagh Arab society's traditional structure is 'white' Arabs, as their castes were defined by profession or scholarly status, not by skin color.
Step-by-step explanation:
The caste that is NOT one of the castes of traditional Azawagh Arab (Nigerian Moor) society is "b) 'white' Arabs". The traditional Azawagh Arab society in West Africa had distinct social classes that included artisans and Islamic scholars, but not a caste based on the color of skin, such as 'white' Arabs. This society was known to be a stratified community where individuals had specific roles and responsibilities. The terms m'alemin and ulama are indeed associated with certain professions or classes within Islamic societies. The m'alemin refers to artisans or blacksmiths, whereas the ulama are Islamic scholars and often healers. The categorization of 'white' Arabs as a caste is not accurate for this specific society.