In a class of 110 students, 68 study Biology, 57 study Chemistry, and 32 study both subjects. How many students study neither Biology nor Chemistry?
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Answer and explanation
Correct answer: 17
Let B denote the Biology group and C denote the Chemistry group. By the inclusion–exclusion principle, n(B ∪ C) = n(B) + n(C) − n(B ∩ C) = 68 + 57 − 32 = 93. Students studying neither subject lie outside this union, so their number is 110 − 93 = 17. Therefore, option A is correct.
Frequently asked questions
What is the correct answer to this question?
17
Why is this the correct answer?
Let B denote the Biology group and C denote the Chemistry group. By the inclusion–exclusion principle, n(B ∪ C) = n(B) + n(C) − n(B ∩ C) = 68 + 57 − 32 = 93. Students studying neither subject lie outside this union, so their number is 110 − 93 = 17. Therefore, option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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