There are 150 students taking Discrete Mathematics II, Calculus II, and Physics I courses. Of these 51 are taking Discrete Mathematics II, 111 are taking Calculus II, and 63 are taking Physics I. There are 41 taking Discrete Mathematics II and Calculus II, 32 students taking Calculus II and Physics I, and 11 students taking Physics I and Discrete Mathematics II. How many of these students are taking exactly two of these three courses?
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just make your usual Venn diagram and start labeling the intersections.
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