Question

In a class of 35 students, 24 like to play cricket and 16 like to play football. Also, each student likes to play at least one of the two games. How many students like to play both cricket and football?

• A. 11
• B. 5
• C. 8
• D. 13

Hint:

Add the individuals and subtract the total to find the "both" category.

Answer 1

The Correct Option is B

Step 1: Concept
The Principle of Inclusion-Exclusion for two sets states: $n(A \cup B) = n(A) + n(B) - n(A \cap B)$.

Step 2: Meaning
Let $A$ be the set of students playing cricket ($n(A)=24$) and $B$ be students playing football ($n(B)=16$). The total students $n(A \cup B)$ is 35.

Step 3: Analysis
Substitute the values into the formula: $35 = 24 + 16 - n(A \cap B)$. This simplifies to $35 = 40 - n(A \cap B)$.

Step 4: Conclusion
$n(A \cap B) = 40 - 35 = 5$. Thus, 5 students play both games. Final Answer: (B)