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Question

# In a class of 55 students, the number of students studying in different subject are, 23 in Mathematics, 24 in physics, 19 in Chemistry, 12 in Mathematics and Physics, 9 in Mathematics and Chemistry, 7 in Physics and Chemistry and 4 in all the three subjects. Find the number of students who have taken exactly one subject.

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Solution

## Given , N=55,n(M)=23,n(P)=24,n(C)=19,n(M∩P)=12,n(P∩C)=7,n(M∩C)=9,n(M∩P∩C)=4Now, number of students studying only Mathematicsn(M∩P′∩C′)=n(M)−n(M∩P)−n(M∩C)+n(M∩P∩C) (by Venn diagram)=23−9−12+4=6Now, number of students studying only Physicsn(P∩M′∩C′)=n(P)−n(P∩M)−n(P∩C)+n(P∩M∩C) (by Venn diagram)=24−12−7+4=9Now, number of students studying only Chemistryn(C∩M′∩P′)=n(C)−n(C∩M)−n(C∩P)+n(M∩P∩C) (by Venn diagram)=19−9−7+4=7So, the number of people who study exactly one of the three subjects =6+9+7=22

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