Question

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

Answer 1

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