In a class, 20 students opted for physics, 17 for Maths, 12 for both physics and maths and 10 students for other subjects. The class contains how many students?
35
Calculating Class Strength: A Step-by-Step Approach
To determine the total number of students in the class, we need to consider students who opted for Physics, those who opted for Maths, those who opted for both, and those who opted for other subjects. We will use the principle of inclusion-exclusion to find the unique count of students taking Physics or Maths, and then add the students taking other subjects.
Understanding the Student Data
- Number of students who opted for Physics (P) = 20
- Number of students who opted for Maths (M) = 17
- Number of students who opted for both Physics and Maths (P & M) = 12
- Number of students who opted for other subjects = 10
Applying the Inclusion-Exclusion Principle
The inclusion-exclusion principle helps us find the total number of unique students who opted for at least one of the two subjects (Physics or Maths). The formula for two sets is:
$\text{n(A} \cup \text{B)} = \text{n(A)} + \text{n(B)} - \text{n(A} \cap \text{B)}$
Here, A represents students opting for Physics and B represents students opting for Maths.
- Number of students opting for Physics or Maths:
- $\text{n(Physics} \cup \text{Maths)} = \text{n(Physics)} + \text{n(Maths)} - \text{n(Physics} \cap \text{Maths)}$
- $\text{n(Physics} \cup \text{Maths)} = 20 + 17 - 12$
- $\text{n(Physics} \cup \text{Maths)} = 37 - 12$
- $\text{n(Physics} \cup \text{Maths)} = 25$
So, 25 students opted for either Physics or Maths (or both, counted once).
Calculating Total Class Students
To find the total number of students in the class, we add the students who opted for Physics or Maths to the students who opted for other subjects.
- Total students in the class = (Students opting for Physics or Maths) + (Students opting for other subjects)
- Total students in the class = $25 + 10$
- Total students in the class = $35$
Summary of Student Distribution
| Category | Number of Students |
|---|---|
| Only Physics | $20 - 12 = 8$ |
| Only Maths | $17 - 12 = 5$ |
| Both Physics and Maths | 12 |
| Other Subjects | 10 |
| Total Class Students | $8 + 5 + 12 + 10 = 35$ |
Therefore, the class contains 35 students.
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