75 persons Major in physics, 83 major in chemistry, 10 not at major in these subjects u want to find number of students majoring in both subjects  Choose the correct option
A) 65
B) 66
C) 67
D) 68
E) 69
Consider the number of total students = n(T) = 100   number of persons Major in physics = n(P) = 75   number of persons Major in chemistry = n(C) = 83   According to the question ;   10 not at major in these subjects = n(P'∩ C') = 10   n(P'∩ C') = n(P U C)' = 10   n(P U C)' = n(T) - n(P U C)   10 = 100 - n(P U C)   n(P U C) = 90   n(P U C) = n(P) + n(C) - n(P ∩ C)   90 = 75 + 83 - n(P ∩ C)   n(P ∩ C) = 158 - 90   n(P ∩ C) = 68   number of students majoring in both subjects WILL be 68   ANSWER:68
<result>D</result>
75 persons Major in physics, 83 major in chemistry, 10 not at major in these subjects u want to find number of students majoring in both subjects