Question

Let M, P and C be the sets of students taking Mathematics, Physics and Computer science respectively in a University. Assume 300 students study Mathematics,350 students study Physics,450 study Computer science ,100 study mathematics and Physics,150 study Mathematics and Computer science ,75 study Physics and Computer science and 10 study all three courses .How many students are taking exactly one of those courses?

Answer 1

Given :-

• n(M) = Students study Mathematics = 300
• n(P) = Students study Physics = 350
• n(C) = Students study Computer Science = 450
• n(M ∩ P) = Students study mathematics and Physics = 100
• n(M ∩ C) = Students study Mathematics and Computer science = 150
• n(P ∩ C) = Students study Physics and Computer science = 75
• n(M ∩ P ∩ C) = Students study all three courses = 10 .

To Find :-

• n( M ∪ P ∪ C ) = Number of students who study exactly one of those courses ?

Formula used :-

• n ( A ∪ B ∪ C ) = n(A) + n(B) + n(C) - n ( A ∩ B ) - n(B ∩ C) - n (A ∩ C) + n( A ∩ B ∩ C )

Solution :-

Putting all values in above formula we get :-

→ n( M ∪ P ∪ C ) = n(M) + n(P) + n(C) - n ( M ∩ P ) - n(P ∩ C) - n (M ∩ C) + n( M ∩ P ∩ C )

→ n( M ∪ P ∪ C ) = 300 + 350 + 450 - 100 - 150 - 75 + 10

→ n( M ∪ P ∪ C ) = 1100 - 325 + 10

→ n( M ∪ P ∪ C ) = 1100 - 315

→ n( M ∪ P ∪ C ) = 785 (Ans.)

Hence, 785 students are taking exactly one of those courses .