source : MGMAT CAT

In a group of 68 students, each student is registered for at least one of three classes - History, Math and English. Twenty-five students are registered for History, twenty-five students are registered for Math, and thirty-four students are registered for English. If only three students are registered for all three classes, how many students are registered for exactly two classes?

13

10

9

8

7

I know there is explanation provided for this but I am not getting the steps.

I started from inside out. There are 3 thhat are in all three classes so

a = number of students in both History and Math

b = number of students in both History and English

c = number of students in both Math and English

For brevity I will only show the first step because herein lies my confusion.

Students in Math Only = 25- (a -3+3+b-3)

The explantion says Students in Math = 25 -(a+b+3) and this is the part that I am missing. Why would we not subtract 3 from the number of students that have both classes?

Can someone please shed some light? Thanks