A survey of 450 students about their subjects of interest resulted in the following outcome.
- 150 students are interest...

Question

A survey of 450 students about their subjects of interest resulted in the following outcome.
- 150 students are interested in Mathematics.
- 170 students are interested in Physics.
- 175 students are interested in Chemistry.
- 60 students are interested in Mathematics and Physics.
- 40 students are interested in Physics and Chemistry.
- 20 students are interested in Mathematics and Chemistry.
- 30 students are interested in Mathematics, Physics, and Chemistry.
- Remaining students are interested in Humanities.
Based on the above information, the number of students interested in Humanities is

A. 10  B. 30  C. 80  D. 45

Accepted Answer

45 students are interested in Humanities. This is a three-set inclusion-exclusion problem. We know the sizes of Math, Physics, and Chemistry circles along with all pairwise intersections and the triple intersection. Inclusion-exclusion gives the total count inside the three circles; subtracting from 450 gives the Humanities students.