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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
- 10
- 30
- 40
- 45
Correct answer: 45
Solution
To find the number of students interested in Humanities, we first calculate the total number of students interested in at least one of the subjects using the principle of inclusion-exclusion. After accounting for overlaps among the subjects, we find that 405 students are interested in Mathematics, Physics, or Chemistry, leaving 45 students who are interested in Humanities.
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