Let A, B, C, D denote, respectively, art, biology, chemistry, and drama courses. Find the number N of students in a dormitory given the data: 12 take A, 5 takeAand B, 4 takeB and D, 2 take B, C,D, 20 take B, 7 takeAand C, 3 takeC and D, 3 take A, C,D, 20 take C, 4 takeAand D, 3 take A, B,C, 2 take all four, 8 take D, 16 takeB and C, 2 take A, B, D, 71 take none.
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Let T be the number of students who take at least one course. By the Inclusion-Exclusion Principle Theorem, where:
Thus T=29, and N=71+T=100.