Question 1017162
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In a class of 32 students,a student is allowed to offer government or history or both. 
If 16 students do government,18 do history and 3 do none of the subjects,find how many do both. 
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Let me reformulate the problem in this way:


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In a group of 29 (=32-3) students 16 students do government and 18 do history; everybody does something; some of them do both.

Find how many do both.
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The answer is: 16 + 18 - 29 = 5.

5 students do both.


For details, see the lesson <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> in this site.

Read attentively this lesson, and you will learn how to solve this kind of problems, once and for all.
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