Van Diagram

[hakyology]

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
Please explain this for me. But actually, I am curious why the formula does not work here with this question.
n(a+b+c) = n(a)+n(b)+n(c)-{n(a+b)+n(b+c)+n(a+c)}-n(a+b+c)

The ansewr is 10

[chidcguy]

The correct formula as I learned 2 days ago is

n(a+b+c) = n(a)+n(b)+n(c)- {n(a+b)+n(b+c)+n(a+c)} + n(a+b+c)

68=25 + 25 + 34 + 3 - {n(a+b)+n(b+c)+n(a+c)}

{n(a+b)+n(b+c)+n(a+c)} = 87-68 =19

The number of Students in exactly 2 sets is {n(a+b)+n(b+c)+n(a+c)} - 3 X n(a+b+c)

19 - 3 X 3 =10

[hakyology]

thank you! however, why did you mutiply 3, could you explain? Thank you.