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??
Answers
48 students studying exactly one of the three subject
Step-by-step explanation:
Total Students = 100
Math = M = 32
Physics P = 20
Biology B = 45
Math and Biology M ∩ B = 15
Math and Physics M ∩ P = 7
Physics and Biology P ∩ B = 10
None of subjects = 30
All subjects = M ∩ B ∩ P = ?
Total = M + P + B - M ∩ B - M ∩ P - P ∩ B + M ∩ B ∩ P + None
=> 100 = 32 + 20 + 45 - 15 - 7 - 10 + M ∩ B ∩ P + 30
M ∩ B ∩ P = 5
Only Maths = M - M ∩ B - M ∩ P + M ∩ B ∩ P = 32 - 15 - 7 + 5 = 15
Only Physics = P - P ∩ B - M ∩ P + M ∩ B ∩ P = 20 - 10 - 7 + 5 = 8
Only Biology = B - M ∩ B - B ∩ P + M ∩ B ∩ P = 45 - 15 - 10 + 5 = 25
Exactly one subject = 15 + 8 + 25
= 48
48 students studying exactly one of the three subject
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