My Math Forum venn diagram

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September 10th, 2011, 06:41 AM   #1
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venn diagram

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September 10th, 2011, 09:39 AM   #2
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Re: venn diagram

Hello, Jungelsucks!

Quote:
 In a street of 150 houses, three different newspapers are delivered. 40 get T. 35 get G. 60 get M. 7 get T and G. 10 get G and M. 4 get T and M. 34 get no papers. How many get all three newspapers?

There are 150 houses and 34 get no newpapers.
Hence, there are 116 houses that get at least one newspaper.

Use this formula:

$n(T \cup G \cup M) \:=\:n(T)\,+\,n(G)\,+\,n(M)\,-\,n(T\cap G)\,-\,n(G\cap M)\,-\,n(T\cap M)\,+\,n(T\cap G\cap M)$

We have:

[color=beige]. . [/color]$116 \;=\;40\,+\,35\,+\,60\,-\,7\,-\,10\,-\,4\,+\,n(T\cap G\cap M) \;\;\;\Rightarrow\;\;\;116 \;=\;114\,+\,n(T\cap G\cap M)$

Therefore:[color=beige] .[/color]$n(T\cap G\cap M) \:=\:2$

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### 150 houses newspapers venn diagram

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