Math Problem Statement
In a study involving 500 students to understand their participation in different extracurricular activities, the following information was gathered: • 410 students participate in one or two of the sports club. • 40 students are only in both the drama and music clubs. • 120 students participate exclusively in the sports club. • 30 students are in both the music and sports clubs. • 220 students are only in music or sports. • 80 students do not participate in any of these three clubs. • 240 students are only in music or drama. Using this information, answer the following questions: i. Draw a Venn diagram to represent the students' participation in these clubs. ii. How many students are involved in all the three clubs? iii. How many students are involved only in exactly two clubs?
Solution
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Math Problem Analysis
Mathematical Concepts
Set Theory
Venn Diagrams
Inclusion-Exclusion Principle
Formulas
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Theorems
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Suitable Grade Level
High School
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