Answer :
Answer:
2 students study all three subjects (Physics, Chemistry, and Biology).
There are a total of 41 students in the group.
Step-by-step explanation:
1. Understanding the Problem:
We’re given information about the number of students studying different combinations of Physics, Chemistry, and Biology. Our goal is to find out:
How many students study all three subjects.
The total number of students in the group.
2. Using a Venn Diagram:
A Venn diagram helps visualize the overlapping sets of students:
Three Circles: We draw three overlapping circles representing Physics, Chemistry, and Biology.
Filling the Overlaps: We start by filling in the sections representing students studying only two subjects and those studying one subject only, based on the given information.
Calculating Missing Values: Using the total number of students for each subject, we work backward to find the missing values, including the number of students studying all three subjects.
3. Finding the Total:
Finally, we add up the numbers in all sections of the Venn diagram to get the total number of students.
The Logic:
The key is to use the “only” information strategically. For example, knowing 7 students study Physics only tells us that this number shouldn’t be included when calculating other combinations involving Physics.
Let me know if you’d like a step-by-step breakdown of the calculations within the Venn diagram!
