If in a class there are 200 students in which 120 take Mathematics, 90 take Physics, 60 take Chemistry, 50 take Mathematics & Physics, 50 take Mathematics & Chemistry, 43 take Physics & Chemistry and 38 take Mathematics, Physics & Chemistry, then the number of students who have taken exactly one subject is
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Let, M 
Mathematics, P 
Physics, C 
Chemistry
Given that total students = 200
n (M) = 120, n (P) = 90, n = 60
n (M 
P) = 50, n (M 
C} = 50, n (P 
C) = 43
n (M 
P 
C) = 38
Required number of students taking exactly one subject is
n (M) + n (P) + n - 2n (M 
P) - 2n (P 
C) - In (M 
C} + 3n (M 
P 
C)
= 120 + 90 + 60-2 (50) - 2 (50) - 2 (43) + 3 (38)
= 98
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