In a group of 50 students 24 like cold drinks and 36 like hot drinks and each student likes at least

Question

In a group of 50 students 24 like cold drinks and 36 like hot drinks and each student likes at least one of the two drinks. How many like both coffee and tea?

Accepted Answer

{"type":"doc","content":[{"content":[{"marks":[{"type":"bold"}],"text":"Step 1 (Set up Set Formula):","type":"text"},{"text":" Let ","type":"text"},{"attrs":{"latex":"C"},"type":"math_inline"},{"text":" be the set of students who like cold drinks, and ","type":"text"},{"attrs":{"latex":"H"},"type":"math_inline"},{"text":" be the set of students who like hot drinks. We are given:","type":"text"}],"type":"paragraph"},{"type":"bullet_list","content":[{"content":[{"content":[{"text":"Total students ","type":"text"},{"attrs":{"latex":"n(C \cup H) = 50"},"type":"math_inline"},{"type":"text","text":" (since each student likes at least one drink)"}],"type":"paragraph"}],"type":"list_item"},{"type":"list_item","content":[{"content":[{"attrs":{"latex":"n(C) = 24"},"type":"math_inline"}],"type":"paragraph"}]},{"content":[{"type":"paragraph","content":[{"type":"math_inline","attrs":{"latex":"n(H) = 36"}}]}],"type":"list_item"}]},{"content":[{"marks":[{"type":"bold"}],"text":"Step 2 (Apply Inclusion-Exclusion):","type":"text"}],"type":"paragraph"},{"type":"math_block","attrs":{"latex":"n(C \cup H) = n(C) + n(H) - n(C \cap H)"}},{"attrs":{"latex":"50 = 24 + 36 - n(C \cap H)"},"type":"math_block"},{"attrs":{"latex":"50 = 60 - n(C \cap H)"},"type":"math_block"},{"attrs":{"latex":"n(C \cap H) = 60 - 50 = 10"},"type":"math_block"},{"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step 3 (Conclusion):"},{"text":" Exactly ","type":"text"},{"marks":[{"type":"code"}],"text":"10","type":"text"},{"type":"text","text":" students like both coffee and tea (both drinks)."}],"type":"paragraph"}]}

Guide / Hint

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