Question 1017162: 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.
Answer by ikleyn(52835)   (Show Source):
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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 Counting elements in sub-sets of a given finite set 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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