Mr. Green teaches band, choir, and math. This year, he has 57 students that take at least one of his classes. He teaches band to 25 students. There are 9 students who have Mr. Green for math and nothing else. Use the Venn diagram below:

Question

A Venn diagram of three overlapping circles titled 'Band,' 'Choir,' and 'Math' is shown.

· The circle on the left titled 'Band' contains the number 11 in the part of the circle that is not overlapping with any other circle.
· The circle on the right titled 'Choir' contains the number 17 in the part of the circle that is not overlapping with any other circle.
· The circle above the other two circles titled 'Math' is empty in the part of the circle that is not overlapping with any other circle.
· The region where all three circles overlap in the middle of the diagram contains the number 3.
· The region where the 'Band' circle overlaps with the 'Math' circle and does not include the intersection of all three circles contains the number 7.

How many students take exactly 2 classes with Mr. Green?

Answer 1

We have the following values from the Venn diagram:
- 11 students take band only
- 17 students take choir only
- 9 students take math only (not included in the diagram)
- 3 students take all three classes
- 7 students take band and math, but not choir

There are 25 students in the band. We know that 11 students take band only, 7 take band and math, and 3 take all three classes. This leaves 25 - 11 - 7 - 3 = 4 students who take band and choir but not math.

Since there are 57 students in total who take at least one class with Mr. Green, there should be 57 - 11 - 17 - 9 - 3 - 7 - 4 = 6 students who take choir and math but not band.

So, the number of students who take exactly 2 classes with Mr. Green is 4 (band and choir) + 7 (band and math) + 6 (choir and math) = 17 students. Answer: \boxed{17}.