document.write( "Question 1176415: In a group of 120 students numbered 1 to 120, all even numbered students choose Physics, students whose numbers are divisible by 5 choose Chemistry and those whose numbers are divisible by 7 choose Economics. How many students choose none of the three subjects? \n" ); document.write( "
Algebra.Com's Answer #803313 by ikleyn(52839)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "In a group of 120 students numbered 1 to 120,
\n" ); document.write( "all even numbered students choose Physics,
\n" ); document.write( "students whose numbers are divisible by 5 choose Chemistry
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\n" ); document.write( "How many students choose none of the three subjects?
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\n" ); document.write( "\n" ); document.write( "            The solution by other tutor is INCORRECT.\r
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\n" ); document.write( "\n" ); document.write( "            I came to bring you the correct solution.\r
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document.write( "We have the sets\r\n" );
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document.write( "    P of  120/2 = 60 students   (Physics)\r\n" );
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document.write( "    C of  120/5 = 24 students   (Chemistry)\r\n" );
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document.write( "    E of  [120/7] = 17 students (Economics)\r\n" );
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document.write( "We have their in-pair intersections\r\n" );
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document.write( "    PC of  120/(2*5)   = 12 students\r\n" );
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document.write( "    PE of  [120/(2*7)] =  8 students\r\n" );
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document.write( "    CE of  [120/(5*7)] =  3 students.\r\n" );
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document.write( "We have their triple intersection\r\n" );
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document.write( "    PCE of 120/(2*5*7) =  1 student.\r\n" );
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document.write( "Now we apply the inclusive-exclusive formula to find the number of students in the UNION of sets (P U C U E)\r\n" );
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document.write( "    n(P U C U E) = n(P) + n(C) + n(E) - n(PC) - n(PE) - n(CE) + n(PCE)  (the alternate sum)\r\n" );
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document.write( "                 = 60 + 24 + 17 - 12 - 8 - 3 + 1 = 79.\r\n" );
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document.write( "The rest of the students,  120 - 79 = 41,  choose NONE of the three subjects.     ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "It is how this problem  SHOULD  BE  solved.\r
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\n" ); document.write( "\n" ); document.write( "It is how this problem  IS  EXPECTED  to be solved.\r
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\n" ); document.write( "\n" ); document.write( "The solution of the other tutor is a  PERFECT  EXAMPLE  of how this problem  SHOULD  NOT  be solved.\r
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\n" ); document.write( "\n" ); document.write( "It is classic example of the typical  ERROR  which  EVERYBODY  MAKES  who is unfamiliar with the right approach.\r
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\n" ); document.write( "\n" ); document.write( "Now you should be  ABSOLUTELY  HAPPY,  because after my post you  KNOW  BOTH\r
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\n" ); document.write( "\n" ); document.write( "how this problem  SHOULD  BE  solved and how you  SHOULD  NOT  even try to approach it.\r
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