document.write( "Question 1185492: A poll was taken of 100 students at a commuter campus to find out how they got to campus. The results were as follows:
\n" ); document.write( "28 said they drove alone.
\n" ); document.write( "31 rode in a carpool.
\n" ); document.write( "30 rode public transportation.
\n" ); document.write( "7 used both carpools and public transportation.
\n" ); document.write( "3 used both a carpool and sometimes their own cars.
\n" ); document.write( "5 used buses as well as their own cars.
\n" ); document.write( "2 used all three methods.
\n" ); document.write( "How many used none of the above-mentioned means of transportation?
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Algebra.Com's Answer #816326 by ikleyn(52781)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "A poll was taken of 100 students at a commuter campus to find out how they got to campus. The results were as follows:
\n" ); document.write( "28 said they drove alone.
\n" ); document.write( "31 rode in a carpool.
\n" ); document.write( "30 rode public transportation.
\n" ); document.write( "7 used both carpools and public transportation.
\n" ); document.write( "3 used both a carpool and sometimes their own cars.
\n" ); document.write( "5 used buses as well as their own cars.
\n" ); document.write( "2 used all three methods.
\n" ); document.write( "How many used none of the above-mentioned means of transportation?
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document.write( "This problem is on the Inclusion-Exclusion pronciple.\r\n" );
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document.write( "You are given the universal set U of 100 students an 3 basic subsets inside it:\r\n" );
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document.write( "    subset A of 28 elements (\"alone\")\r\n" );
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document.write( "    subset C of 31 elements (\"carpool\")\r\n" );
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document.write( "    subset P of 30 elements (\"public transportation\")\r\n" );
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document.write( "You also given their in-pair intersections  \r\n" );
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document.write( "    subset AC of 3 elements (used both a carpool and sometimes their own cars)\r\n" );
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document.write( "    subset CP of 7 elements (used both carpools and public transportation)\r\n" );
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document.write( "    subset AP of 5 elements (used buses as well as their own cars)\r\n" );
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document.write( "Finally, you are given that the triple intersectio ACP  has 2 elements.\r\n" );
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document.write( "Using the exclusive-inclusive priinciple, you can find the number of students in the UNION of the subsets A U C U P\r\n" );
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document.write( "    n(A U C U P) = n(A) + n(c) + n(P) - n(AC) - n(AP) - n(CP) + n(ACP) = \r\n" );
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document.write( "                 =  28  + 31   +30    -   3   -  7    -  5    +  2 = 76.\r\n" );
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document.write( "The rest,   100 - 76 = 24  belong to the cathegory under the problem's question.\r\n" );
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\n" ); document.write( "\n" ); document.write( "On inclusion-exclusion principle,  see this Wikipedia article\r
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\n" ); document.write( "\n" ); document.write( "https://en.wikipedia.org/wiki/Inclusion%E2%80%93exclusion_principle\r
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\n" ); document.write( "\n" ); document.write( "To see many other similar  (and different)  solved problems,  see the lessons\r
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\n" ); document.write( "\n" ); document.write( "    - Counting elements in sub-sets of a given finite set\r
\n" ); document.write( "\n" ); document.write( "    - Advanced problems on counting elements in sub-sets of a given finite set\r
\n" ); document.write( "\n" ); document.write( "    - Challenging problems on counting elements in subsets of a given finite set \r
\n" ); document.write( "\n" ); document.write( "    - Selected problems on counting elements in subsets of a given finite set \r
\n" ); document.write( "\n" ); document.write( "    - Inclusion-Exclusion principle problems \r
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\n" ); document.write( "\n" ); document.write( "Happy learning (!)\r
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