Discussion
A survey of 450 students about their subjects of interest resulted in the following outcome.
- 150 students are interested in Mathematics.
- 200 students are interested in Physics.
- 175 students are interested in Chemistry.
- 50 students are interested in Mathematics and Physics.
- 60 students are interested in Physics and Chemistry.
- 40 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
Answer: D
The number interested in Humanities is 45.
By inclusion and exclusion, the students interested in at least one of the three sciences are
\[ \begin{aligned} &150 + 200 + 175 - 50 - 60 - 40 + 30 \\ &= 525 - 150 + 30 = 405 \end{aligned} \]
The remaining \(450 - 405 = 45\) are interested in Humanities. The triple overlap must be added back because subtracting the three pairwise overlaps removes the 30 students interested in all three subjects once too often. 30 and 40 are figures taken from the list, and 10 does not come from any consistent count.
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