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 determine the number of students who participate in neither football nor cricket, the principle of inclusion-exclusion will be applied.

1. Data Initialization:

- Total student count: 50
- Students engaged in football (F): 30
- Students engaged in cricket (C): 25
- Students engaged in both football and cricket (F ∩ C): 10
- Students engaged in football or cricket or both (F ∪ C): Calculated as F + C - (F ∩ C)

2. Calculation of Students Participating in at Least One Sport:

[ |F ∪ C| = 30 + 25 - 10 = 45 ]

3. Calculation of Students Participating in Neither Sport:

[ Students playing neither = Total - |F ∪ C| = 50 - 45 = 5 ]

Final Result:

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