document.write( "Question 1165301: A survey of 250 SPC students was taken at registration. Of those surveyed:\r
\n" ); document.write( "\n" ); document.write( "63 students had signed up for a Math course
\n" ); document.write( "50 students had signed up for a Language Arts course
\n" ); document.write( "21 students had signed up for both a Math and Language Arts course
\n" ); document.write( "8 students had signed up for both a Math and Humanities course
\n" ); document.write( "5 students had signed up for both a Language Arts and Humanities course
\n" ); document.write( "1 students had signed up for all three courses
\n" ); document.write( "2 students did not sign up for any of these classes
\n" ); document.write( "How many students signed up for only Humanities (of these three)? \n" ); document.write( "
Algebra.Com's Answer #789808 by ikleyn(52787)\"\" \"About 
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\n" ); document.write( "A survey of 250 SPC students was taken at registration. Of those surveyed:
\n" ); document.write( "63 students had signed up for a Math course
\n" ); document.write( "50 students had signed up for a Language Arts course
\n" ); document.write( "21 students had signed up for both a Math and Language Arts course
\n" ); document.write( "8 students had signed up for both a Math and Humanities course
\n" ); document.write( "5 students had signed up for both a Language Arts and Humanities course
\n" ); document.write( "1 students had signed up for all three courses
\n" ); document.write( "2 students did not sign up for any of these classes
\n" ); document.write( "How many students signed up for only Humanities (of these three)?
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document.write( "We have an universal set U of 250 students\r\n" );
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document.write( "    and its subsets\r\n" );
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document.write( "M of 63 students;\r\n" );
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document.write( "L of 50 students;\r\n" );
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document.write( "H of unknown number of students;\r\n" );
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document.write( "   their in-pairs intersections\r\n" );
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document.write( "ML of 21 students;\r\n" );
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document.write( "MH of  8 students\r\n" );
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document.write( "LH of 5 students\r\n" );
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document.write( "    and finally their triple intersection\r\n" );
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document.write( "MHL of 1 student.\r\n" );
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document.write( "Based on this info, we can easily write an equation for the number of students who takes at least one of the three cources\r\n" );
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document.write( "    n(M U L U U) = m(M) + n(L) + n(H) - n(M ∩ L) - n(M ∩ H) - n(L ∩ H) + n(M ∩ L ∩ H). \r\n" );
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document.write( "In this equation, the left side is 250-2 = 248.\r\n" );
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document.write( "In the right side, you know all the terms except of n(H), which I am going to find now.\r\n" );
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document.write( "Substituting all known terms, you get\r\n" );
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document.write( "    248 = 63 + 50 + n(H) - 21 - 8 - 5 + 1.\r\n" );
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document.write( "From this equation,\r\n" );
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document.write( "    n(H) = 248 - 63 - 50 + 21 + 8 + 5 - 1 = 168.\r\n" );
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document.write( "Now, to find n(H only), we should subtract n(MH) and n(LH) from n(H) and add n(MHL):\r\n" );
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document.write( "    n(H only) = 168 - 8 - 5 + 1 = 156.     ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "In order for to see many other similar solved problems with detailed explanations,  look into the lessons\r
\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( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "Look also into the links\r
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\n" ); document.write( "\n" ); document.write( "https://www.algebra.com/algebra/homework/sets-and-operations/sets-and-operations.faq.question.1149313.html\r
\n" ); document.write( "\n" ); document.write( "https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1132870.html\r
\n" ); document.write( "\n" ); document.write( "https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1129554.html\r
\n" ); document.write( "\n" ); document.write( "https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1129554.html\r
\n" ); document.write( "\n" ); document.write( "https://www.algebra.com/algebra/homework/Rate-of-work-word-problems/Rate-of-work-word-problems.faq.question.1126097.html\r
\n" ); document.write( "\n" ); document.write( "https://www.algebra.com/algebra/homework/word/evaluation/Evaluation_Word_Problems.faq.question.1126099.html\r
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\n" ); document.write( "\n" ); document.write( "to similar solved problems in the archive of this forum.\r
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