Solution to In a class of 32 students, 18 offers chemistry, 16 offers Physics 22 offer Mathematics. … - Sikademy
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Archangel Macsika

In a class of 32 students, 18 offers chemistry, 16 offers Physics 22 offer Mathematics. 6 offer all three subjects, 3 offer Chemistry and Physics only and 5 offer only physics only. Each student offers at least one subject. Find the number of student who offer A. chemistry only B. only one student C. only two subjects

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N(P)=16, P(C)=18, P(M)=22


N(P\cap C\cap M)=6

N(P\cap C \cap M^C)=3

N(P\cap C^C \cap M^C)=5

N(P\cap M \cap C^C)=N(P)-N(P\cap C\cap M)-

-N(P\cap C \cap M^C)-N(P\cap C^C \cap M^C)

=16-6-3-5=2

N(P\cup C\cup M)=N(P)+N(M)+N(C)

-N(P\cap M \cap C^C)-N(P\cap C \cap M^C)-

-N(C\cap M \cap P^C)-2N(P\cap C\cap M)

N(C\cap M \cap P^C)=16+18+22

-32-3-2-2(6)=7


A. N(C\cap P^C\cap M^C)=2


B. N(\text{only one subject})=5+2+7=14


C. N(\text{only two subjects})=3+2+7=12

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