Question 437581: 55 freshman were interviewed about the classes they were taking this semester.
21 said they were taking math.
15 said they were taking english.
26 said they were taking science.
8 said they were taking both science and math.
6 said they were taking both science and english.
3 said they were taking both math and english.
2 said they were taking all three classes.
How many students are not taking any science, math, or english?
How many students are taking exactly one of science, math, or english?
Answer by robertb(5830)   (Show Source):
You can put this solution on YOUR website! No Venn Diagrams needed here, just the General addition law for counting:
N(m U e U s) = N(m) + N(e) + N(s) - N(me)- N(sm) - N(se) + N(mes) = 21 + 15 + 26 - 3 - 8 - 6 + 2 = 47 students are taking exactly one of science, math, or English.
55 - 47 = 8 are not taking any science, math, or English.
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