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In a survey of 1000 students, 607 like chocolate ice cream 491 like vanilla ice cream ● 394 like strawberry ice cream . 300 like both chocolate and vanilla . 238 like both chocolate and strawberry • 201 like both vanilla and strawberry • 124 like none of these flavors How many students like all three flavors? Enter the exact integer. ●

In a survey of 1000 students, 607 like chocolate ice cream 491 like vanilla ice cream ● 394 like strawberry ice cream . 300 like both chocolate and vanilla . 238 like both chocolate and strawberry • 201 like both vanilla and strawberry • 124 like none of these flavors How many students like all three flavors? Enter the exact integer. ●

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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In a survey of 1000 students, 607 like chocolate ice cream .491 like vanilla ice cream • 394 like strawberry ice cream . 300 like both chocolate and vanilla . 238 like both chocolate and strawberry . 201 like both vanilla and strawberry • 124 like none of these flavors How many students like all three flavors? Enter the exact integer. Hint 1: The principle of inclusion-exclusion for three sets is: |CUVUS| = |C| + IV+ |S| - |CV-CnS-VOS+Cnvns Now, convince yourself with a Venn diagram that by adding (CUVUS)| (the number of students who liked none of these flavors) to both sides of this equation, that the LHS will equal 1000 (each student either liked at least one of the three flavors or did not). The only missing value then becomes |Cnvn S, the number of students who liked all three flavors. If you do draw a Venn diagram, filling in the regions with the appropriate numbers, it is good to check that your work matches the given information. Hint 2: Alternatively, find |CUVU S using the number of students who liked none of the flavors and the fact that there are 1000 students in the universal set. This is similar to how we did the example in the slides.
Transcribed Image Text:In a survey of 1000 students, 607 like chocolate ice cream .491 like vanilla ice cream • 394 like strawberry ice cream . 300 like both chocolate and vanilla . 238 like both chocolate and strawberry . 201 like both vanilla and strawberry • 124 like none of these flavors How many students like all three flavors? Enter the exact integer. Hint 1: The principle of inclusion-exclusion for three sets is: |CUVUS| = |C| + IV+ |S| - |CV-CnS-VOS+Cnvns Now, convince yourself with a Venn diagram that by adding (CUVUS)| (the number of students who liked none of these flavors) to both sides of this equation, that the LHS will equal 1000 (each student either liked at least one of the three flavors or did not). The only missing value then becomes |Cnvn S, the number of students who liked all three flavors. If you do draw a Venn diagram, filling in the regions with the appropriate numbers, it is good to check that your work matches the given information. Hint 2: Alternatively, find |CUVU S using the number of students who liked none of the flavors and the fact that there are 1000 students in the universal set. This is similar to how we did the example in the slides.
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