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