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500 students enrolled in at least 2 of 3 classes

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500 students enrolled in at least 2 of 3 classes: English, Math, History. 150 students enrolled in both history and English, 300 enrolled in math & history, 170 enrolled in both math and English. How many of the 500 students are enrolled in all three classes?

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The solution provides detailed and step-by-step instructions that determine how many of the 500 students are enrolled in all three classes.

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If two events A and B are independent, then the probability of both events is the product of the probabilities for each event:
P(A and B) = P(A)P(B).

Let call E = event that students enrolled in English
Let call M = event that students ...

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