There are math english physics chemistry four subjects for s

There are math, english, physics, chemistry, four subjects for students to take. Suppose the number of people taking the subjects are as following:
M: 10,
E: 12,
C: 9,
P:8,
M n E: 8,
M n C: 6,
M n P: 4,
E n C: 6,
E n P: 5,
C n P: 4,
nobody take more than 2 subjects. How many people take at least one subject?

Solution

Atleast one subject = Set AUBUC

n(AUBUC) = n(A)+n(B)+n(C_-n(AB)-n(BC)-n(CA)+n(ABC)

Substitute for the above from the given data and remember n(ABC) =0 as no body has taken more than 2 subjects.

n(MUEUCUP) = 10+12+9+8-(8+6+4+6+5+4)+0-0

= 39-33

=6