Solution: Using the principle of inclusion-exclusion for three sets \( M \), \( P \), and \( C \), we have:
\[ |M \cup P \cup C| = |M| + |P| + |C| - |M \cap P| - |P \cap C| - |M \cap C| + |M \cap P \cap C| \]
Given:
Since \(|M \cup P \cup C| = 40\), substitute the values and solve for \(|M \cap P \cap C|\):
\[ 40 = 20 + 25 + 16 - 11 - 15 - 10 + x \]
\[ x = 10 \]
Thus, the maximum number of students who passed in all three subjects is 10.
In the following figure, four overlapping shapes (rectangle, triangle, circle, and hexagon) are given. The sum of the numbers which belong to only two overlapping shapes is ________
The table shows the data of 450 candidates who appeared in the examination of three subjects – Social Science, Mathematics, and Science. How many candidates have passed in at least one subject?
How many candidates have passed in at least one subject?
Match List-I with List-II: List-I