53 freshman were interviewed about the classes they were taking this semester 24 said they were taking science 22 said they were taking math 17 said they were taking English 7 said they were taking both science and math 10 said they were taking both math and English 4 said they were taking both math and English 2 said they were taking all three classes

The questions are:

How many students are not taking any science, math, or English? AND

How many students are taking exactly one of science, math, or English classes?

This is best answered using a Venn diagram. If you look at the separate areas, you see there are 7 areas.

The common area is the two students who takes the three classes.

4 said they were taking both math and English

4 - 2 = 2 only take math & English

7 said they were taking both science and math

7 - 2 = 5 only take math and science

10 said they were taking both science and English

10 - 2 = 8 only take science and English

17 said they were taking English

17 - (2 + 8 + 2) = 5 take only English

22 said they were taking math

22 - (2 + 5 + 2) = 13 take math

24 said they were taking science

24 - (2 + 8 + 5) = 9 only take science

Adding them all up:

2 + 9 + 13 + 5 + 8 + 5 + 2 = 44

So, 44 students are taking the 3 courses

53 - 44 = 9 students are not taking any of the 3 courses

5 + 13 + 9 = 27 take only 1 of these courses