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

Rationale: 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 : d
Answer: D