Question 1126097
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I just solved a TWIN problem for you under the link 


<A HREF=https://www.algebra.com/algebra/homework/word/evaluation/Evaluation_Word_Problems.faq.question.1126099.html>https://www.algebra.com/algebra/homework/word/evaluation/Evaluation_Word_Problems.faq.question.1126099.html</A>


https://www.algebra.com/algebra/homework/word/evaluation/Evaluation_Word_Problems.faq.question.1126099.html




This time the situation is very similar:


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;You are given 3 sets (the number of elements in three sets M, H and G);


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;You are given the numbers of elements in their in-pair intersections (M n H), (M n G)  and  (H n G);


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;and finally, you are given the numbers of elements in the triple intersection (M n H n G).


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;They ask you about the number of elements in the union of the three sets  (M U H U G).



The same formula &nbsp;(*) &nbsp;works as in my previous post:


<pre>
    n(M U H U G) = n(M) + n(H) + n(G) - n(M n H) - n(M n G) - n(H n G) + n(M n H n G).        (*)


you only need to substitute the given data and calculate:


    n(M U H U G) = 50 + 60 + 70 - 25 - 28 - 32 + 21 = 116.


<U>Answer</U>.   The number of peoples who failed at least one subject is 116.
</pre>

Solved.


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This time I will not prove the formula &nbsp;(*) &nbsp;here:  &nbsp;&nbsp;it is just proved under the referred link.


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For many other solved similar problems 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>

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

in this site.