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In a freshmen high school class of 400 students, 110 take math, 130 take English, 150...

In a freshmen high school class of 400 students, 110 take math, 130 take English, 150 take history, 30 take math and English, 40 take math and history, 50 take English and history, and 280 take math or English or history. If a freshmen strudent is picked at random from the class, then, for k=0,1,2,3, find the probability that:

a. He takes exactly k of the named subjects.

b. He takes at least k of the named subjects.

c. He takes no more than k of the named subjects.

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