in a class of 55 students ,the number of students arising different subjects are 23 in mathematics, 24 in physics, 19 in chemistry ,12 in mathematics and physics and chemistry and 4 In all the three subjects the number of students who have taken exactly one subject is
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Total no. of student=55
Let n(M)=student who studying mathematics
n(C)=student who studying chemistry
n(P)=student who studying Physics
∴n(M)=23,n(P)=24,n(C)=19,n(M∩P)=12,n(M∩C)=9,n(P∩C)=7,n(M∩P∩C)=4
Number of student who studying mathematics but not physic and chemistry
⇒n(M)−[(n(M∩C)+n(M∩P)]+n(M∩P∩C)
⇒23−[9+12]+4
⇒23−21+4=6
Number of student who studying chemistry but not physic and matehematics
⇒n(C)−[(n(M∩C)+n(P∩C)]+n(M∩P∩C)
⇒19−[9+7]+4
⇒19−16+4=7
Number of student who studying physics but not mathematics and chemistry
⇒n(P)−[(n(M∩P)+n(P∩C)]+n(M∩P∩C)
⇒24−[12+7]+4
⇒24−19+4=9
∴no. of student studying exactly one subject=6+7+9=22
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