Based on the above information, the number of students interested in Humanities is
Calculating Humanities Interest Using Set Theory
This problem involves finding the number of students interested in Humanities, which represents the students outside the sets of Mathematics, Physics, and Chemistry interests. We use the Principle of Inclusion-Exclusion.
Given Information
- Total students: 450
- Mathematics (M): 150
- Physics (P): 200
- Chemistry (C): 175
- Mathematics and Physics ($M \cap P$): 50
- Physics and Chemistry ($P \cap C$): 60
- Mathematics and Chemistry ($M \cap C$): 40
- Mathematics, Physics, and Chemistry ($M \cap P \cap C$): 30
Applying Inclusion-Exclusion Principle
First, calculate the total number of students interested in at least one of Mathematics, Physics, or Chemistry ($|M \cup P \cup C|$).
The formula is:
$|M \cup P \cup C| = |M| + |P| + |C| - (|M \cap P| + |P \cap C| + |M \cap C|) + |M \cap P \cap C|$Substitute the given values:
$|M \cup P \cup C| = 150 + 200 + 175 - (50 + 60 + 40) + 30$ $|M \cup P \cup C| = 525 - (150) + 30$ $|M \cup P \cup C| = 525 - 150 + 30$ $|M \cup P \cup C| = 375 + 30$ $|M \cup P \cup C| = 405$So, 405 students are interested in at least one of the three subjects (Mathematics, Physics, or Chemistry).
Determining Humanities Interest
The students interested in Humanities are those remaining students who are not interested in Mathematics, Physics, or Chemistry.
Number of Humanities students = Total students - $|M \cup P \cup C|$
$ \text{Humanities} = 450 - 405 $ $ \text{Humanities} = 45 $Therefore, 45 students are interested in Humanities.
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