Question

in a survey of 200 students in a school it was found that 120 study mathematics 90 study physics and 70 study chemistry,40study mathematics and physics 30 study physics and chemistry 50 study chemistry and mathematics and 20 non of these subjects .find the number of the students who study only mathematics.​

Answer 1

Let M, P and C denote the students studying Mathematics, Physics and Chemistry

And U represents total students

So, n(U)=200,

n(M)=120,n(P)=90

n(C)=70,n(M∩P)=40,n(P∩C)=30

n(M∩C)=50,n(M∪P∪C)

′

=20

∴n(M∪P∪C)

′

=n(U)−n(M∪P∪C)

⇒20=200−n(M∪P∪C)

⇒n(M∪P∪C)=180

⇒n(M∪P∪C)=n(M)+n(P)+n(C)

−n(M∩P)−n(P∩C)−n(C∩M)+n(C∩M∩P)

∴180=120+90+70−40−30−50+n(C∩M∩P)

⇒180=280−120+n(C∩M∩P)

⇒n(P∩C∩M)=300−280=20

Hence, the number of students studying all three subjects is 20.

Hope this helps you

Answer 2

Answer:

nice question........