Question 1100288
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<pre>
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.
</pre>


On this subject see the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/misc/Counting-elements-in-sub-sets-of-a-given-finite-set.lesson>Counting elements in sub-sets of a given finite set</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/misc/Advanced-probs-counting-elements-in-sub-sets-of-a-given-finite-set.lesson>Advanced problems on counting elements in sub-sets of a given finite set</A>

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 . . .