Question

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 ​

Answer 1

Step-by-step explanation:

ANSWER

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