Question

In a college, 60 students enrolled in chemistry, 40 in physics, 30 in biology, 15 in chemistry and physics, 10 in physics and biology, and 5 in biology and chemistry. No one is enrolled in all three. How many are enrolled in at least one subject?

Answer 1

We are given n(C)=60 , n(P)=40 and n(B)=30

n(C∩P)=15 , n(P∩B)=10 , n(B∩C)=5

Since n(C∩P∩B)=0

The required answer is n(C∪P∪B∪)

n(C∪P∪B∪)=n(C)+n(P)+n(B)−n(C∩P)−n(P∩B)−n(B∩C)+n(C∩B∩P)

⇒n(C∪P∪B∪)

=60+40+30−15−10−5=100