Machine model, goal model, equilibrium model and professional model are the approaches used in the analysis of:

To solve this question, the user needs to have knowledge of the different approaches used in analyzing various systems.

Machine model, goal model, equilibrium model, and professional model are the approaches used in the analysis of organizations.

Option A is incorrect because while institutions can also be analyzed, these four models are not commonly used in analyzing institutions.

Option B is correct because the four models mentioned are commonly used in analyzing organizations, which can be defined as a group of people working together in a structured and coordinated way to achieve specific goals or objectives.

Option C is incorrect because although associations can also be analyzed, these four models are not commonly used in analyzing associations.

Option D is incorrect because social facts refer to the aspects of social life that can be observed and measured objectively, and these models are not used to analyze social facts.

Therefore, the correct answer is:

The Answer is: B. organizations.