Final answer:
The question involves calculation of probabilities related to part-time students and distance learning classes, a topic in the field of mathematics, specifically probability and statistics.
Step-by-step explanation:
The subject of this question is Mathematics, specifically related to probability and statistics, as it deals with the analysis of part-time students and those enrolled in distance learning classes. Given that 10 percent of all students have taken a distance learning class (Event D), and 40 percent are part-time students (Event E), with 20 percent of part-time students also having taken a distance learning class, we are looking at the intersection of these two events.