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

Use the inclusion-exclusion principle to find the number of students playing at least one sport: \[ n(\text{Football} \cup \text{Cricket}) = n(\text{Football}) + n(\text{Cricket}) - n(\text{Both}) \] \[ = 30 + 25 - 10 = 45 \] Total students = 50. Students playing neither are: \[ 50 - 45 = 5 \] Thus, the number of students playing neither is: \[ \boxed{5} \]