SOLUTION: In a survey of 100 students, the numbers taking various courses were found to be English, 70; mathematics, 45; chemistry, 60; English and mathematics, 30; English and chemistry, 38

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Question 1100288: In a survey of 100 students, the numbers taking various courses were found to be English, 70; mathematics, 45; chemistry, 60; English and mathematics, 30; English and chemistry, 38; mathematics and chemistry, 36; and courses in all three areas, 23.
Found 2 solutions by ikleyn, richwmiller:
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
Then the number of students of those 100 surveyed who took at least one course was

70 + 45 + 60 - (30+38+36) + 23 = 94,


and the number of those who took NO ONE of these courses was 100-94 = 6.


On this subject see the 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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It is a beautiful problem, and I like to explain it to students in all details, but this time I was partly upset
by not seeing a question in your post . . .



Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
I like to see it as a Venn diagram
t-A+B+C-abt-bct-act+abc=o
100-94=6