Question

6. Out of 300 students in a class, 60% students study Physics, 35% students study
Chemistry and 20% students do not study both of the subjects.

i. How many students study both subjects?
ii. How many students study Physics only?
iii. How many students study Chemistry only?
​

Answer 1

Answer: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)=4

Now, number of students studying only Mathematics

n(M∩P  

′

∩C  

′

)=n(M)−n(M∩P)−n(M∩C)+n(M∩P∩C)    (by Venn diagram)

=23−9−12+4=6

Now, number of students studying only Physics

n(P∩M  

′

∩C  

′

)=n(P)−n(P∩M)−n(P∩C)+n(P∩M∩C)    (by Venn diagram)

=24−12−7+4=9

Now, number of students studying only Chemistry

n(C∩M  

′

∩P  

′

)=n(C)−n(C∩M)−n(C∩P)+n(M∩P∩C)    (by Venn diagram)

=19−9−7+4=7

So, the number of people who study exactly one of the three subjects =6+9+7=22

Step-by-step explanation: