A school has 75 students. Of these, 32 students take part in music and 28 take part in drama. If 10 students take part in both activities, how many students take part in neither activity?
Answer and explanation
Correct answer: 25
Let \(M\) be the music group and \(D\) the drama group. By inclusion–exclusion, \(n(M\cup D)=n(M)+n(D)-n(M\cap D)=32+28-10=50\). Thus 50 students participate in at least one activity. The number participating in neither is \(75-50=25\), so option B is correct. The overlap is subtracted once because it was counted twice.
Frequently asked questions
What is the correct answer to this question?
25
Why is this the correct answer?
Let \(M\) be the music group and \(D\) the drama group. By inclusion–exclusion, \(n(M\cup D)=n(M)+n(D)-n(M\cap D)=32+28-10=50\). Thus 50 students participate in at least one activity. The number participating in neither is \(75-50=25\), so option B is correct. The overlap is subtracted once because it was counted twice.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
