Question

In a class of 50 students, 30 play football, 25 play cricket, and 10 play both. How many students play neither?

• A. 5
• B. 10
• C. 15
• D. 20

Hint:

For problems involving overlapping sets, use the formula \( n(A \cup B) = n(A) + n(B) - n(A \cap B) \) to find students in at least one category, then subtract from the total.

Answer 1

The Correct Option is A

To solve the problem, we need to find how many students play neither football nor cricket using the principle of inclusion-exclusion.

1. Understanding the Concepts:

- Total students = 50
- Students playing football (F) = 30
- Students playing cricket (C) = 25
- Students playing both (F ∩ C) = 10
- Students playing football or cricket or both (F ∪ C) = F + C - (F ∩ C)

2. Calculate Students Playing Football or Cricket:

\[ |F \cup C| = 30 + 25 - 10 = 45 \]

3. Calculate Students Playing Neither:

\[ \text{Students playing neither} = \text{Total} - |F \cup C| = 50 - 45 = 5 \]

Final Answer:

The number of students who play neither football nor cricket is 5.