Question

in a class of 30 students, 18 students play basketball and 15 students play soccer. if 5 students play neither sport, how many students play both basketball and soccer?
o a. 3
o b. 5
o c. 8
o d. 12

Explanation:

Step1: Find number of students who play at least one sport

Total students - students who play neither sport. So, $30 - 5=25$ students play at least one sport.

Step2: Apply the inclusion - exclusion principle

Let $A$ be the set of basketball - playing students and $B$ be the set of soccer - playing students. The formula is $|A\cup B|=|A| + |B|-|A\cap B|$. We know $|A\cup B| = 25$, $|A| = 18$, and $|B| = 15$. Substitute these values: $25=18 + 15-|A\cap B|$.

Step3: Solve for $|A\cap B|$

First, simplify the right - hand side: $18 + 15=33$. Then, we have $25=33-|A\cap B|$. Rearranging gives $|A\cap B|=33 - 25=8$.

Answer:

C. 8