Solution to Let A, B, C, D denote, respectively, art, biology, chemistry, and drama courses. Find the … - Sikademy
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Archangel Macsika

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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Solution:

Let T be the number of students who take at least one course. By the Inclusion-Exclusion Principle Theorem, T=s_{1}-s_{2}+s_{3}-s_{4} where:

\begin{array}{ll} s_{1}=12+20+20+8=60, & s_{2}=5+7+4+16+4+3=39, \\ s_{3}=3+2+2+3=10, & s_{4}=2 . \end{array}

Thus T=29, and N=71+T=100.


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