In a class of 30 students, 18 play soccer, 12 play basketball, and 5 play both. How many students play neither sport?
["How Many Students in a Class of 30 Play Neither Soccer Nor Basketball?", "In any group of students, it’s common to analyze participation in activities like sports. Take, for example, a class of 30 students where some enjoy soccer, basketball, or both. Understanding how many students engage in these activities—and how many stay on the sidelines—is valuable for school planners, coaches, and educators.", "The Breakdown of Student Participation", "- Total students: 30\n- Students who play soccer: 18\n- Students who play basketball: 12\n- Students who play both soccer and basketball: 5", "At first glance, it might seem that 18 + 12 = 30 students play sports—but this overcounts those who play both sports. To find the actual number of students who play either soccer or basketball (or both), we use the principle of inclusion-exclusion:", "[\n\ ext{Students who play soccer or basketball} = \ ext{Soccer} + \ ext{Basketball} - \ ext{Both}\n]\n[\n= 18 + 12 - 5 = 25\n]", "So, 25 students play at least one of the two sports.", "Calculating Students Who Play Neither", "Now, subtract this number from the total class size:", "[\n\ ext{Students who play neither} = \ ext{Total students} - \ ext{Students who play soccer or basketball}\n]\n[\n= 30 - 25 = 5\n]", "Conclusion", "Out of 30 students, 5 students play neither soccer nor basketball. This insight helps schools allocate resources wisely—perhaps introducing new activities to engage the 5 who remain uninvolved, or optimizing schedules to minimize conflicts between sports.", "Understanding student participation patterns supports inclusive and effective physical education programs in classrooms and communities alike."]
