Question

Among 100 students 32 study math,20 study physics,45 study Biology, 15 study Math and Biology, 7 study Math and Physics, 10 study Physics and Biology and 30 do not study any of the subject.
Find the number of students studying exactly one of the three subject??​

Answer 1

Answer is 48 Students

Step-by-step explanation:

• Let M, P, B denote the set of students studying Maths, Physics and Biology respectively.  

• In order to find the number of students studying exactly one of the subjects, we need to draw the Venn Diagram and use it further to find the solution.

As in the figure, (attached for reference)

• 5 are studying all subjects

• 7 - 5 = 2 study Maths and Physics but not all three

• 15 - 5 = 10 study Maths and Biology But not all three

• 10 - 5 = 5 study Biology and Physics But not all three

• 32 - (10 + 2 + 5) = 15 study Maths Only

• 20 - (2 + 5 + 5) = 8  study Physics Only

• 45 - (10 + 5 + 5) = 25 study Biology Only  

Hence, Number of Students studying exactly one of the three subjects = 15 + 8 + 25 = 48

Answer 2

Among 100 students 32 study mathematics,20 study physics,45 study biology,15 study mathematics and biology, 7 study mathematics and physics,10 study physics and biology and 30 do not study any of the three subjects.

Find he number of students studying all three subjects.

Find the number of students studying exactly one of the three subjects.

Draw a Venn diagram and fill all the regions.