Question 1119714: A person applying for the position of college registrar submitted the following report to the college president on 101 students: 31 take math, 28 take chemistry; 42 take psychology; 9 take math and chemistry; 10 take chemistry and psychology; 6 take math and psychology; 4 take all three subjects; and 20 take none of these courses. What is wrong with this scenario?
Answer by ikleyn(52787)   (Show Source):
You can put this solution on YOUR website! .
If the data is correct, then the following identity must be in place:
M + C + P - MC - CP - MP + MCP + 20 = 101. (1) <<<---=== It is the GLOBAL balance equation
(where M = 31, C = 28, P = 42, 9 = MC, 10 = CP, 6 = MP, 4 = MCP, with obvious abbreviations).
But if you substitute the values into the formula (1), your left side will be 100; not 101.
It means that the data is FALSE.
But this check does not give the answer which part is wrong.
Everything might be wrong.
But the minimal correction is to assume that the number 20 is wrong.
If to replace it with 21 (instead of 20), the balance will be correct.
If you are interested to learn more on the subject, read these two lessons
- Counting elements in sub-sets of a given finite set
- Advanced problems on counting elements in sub-sets of a given finite set
in this site.
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