16. 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?

[tex[ two groups=-68+25+25+34 -6=10[/tex]

Step-by-step explanation:

For this case we have a diagram of the situation on the figure attached.

And for this case we can us the following rule from probability:

Or equivalently:

We know the total on this case total=68, the people for history is A=25, for math B=25 and for english C=34, and the people in all the groups 3, so we can replace:

And if we solve for the poeple in two groups we got:

[tex[ two groups=-68+25+25+34 -6=10[/tex]

well

44-3-3-3=35

35+4+4+4+4=51

so the ansewr would be 51 degreesat 7: 00