document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=255058>Question 255058</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a group of 28 students, 11 are taking math, 19 are taking English, 12 are taking history, 6 are taking math and history, 9 are taking history and English, 7 are taking math and English, and 5 are taking all three subjects.\r<BR>\n" );
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document.write( "(a) How many of the students are not taking any of the three subjects?<BR>\n" );
document.write( "(b) How many of the students are taking only math?<BR>\n" );
document.write( "(c) How many of the students are taking only one of these subjects?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #187338 by </B><A HREF=/tutors/aboutme.mpl?userid=Greenfinch><B>Greenfinch(383)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Greenfinch><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Greenfinch><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=187338\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is clearer if you do a Venn diagram. Anyway, here are the numbers.<BR>\n" );
document.write( "M + H + E = 5<BR>\n" );
document.write( "so M + H = 6 and therefore 1 is just doing M + H<BR>\n" );
document.write( "and M + E = 7 therefore 2 are just doing M + E<BR>\n" );
document.write( "and E + H = 9 therefore 4 are just doing E + H<BR>\n" );
document.write( "11 are doing M from which you subtract the 5 doing all, the 1 doing M + H and the 2 doing M + E giving 3 just doing M<BR>\n" );
document.write( "12 are doing H from which you subtract the 5 doing all, the 1 doing M + H and the 4 doing E + H giving 2 just doing H<BR>\n" );
document.write( "19 are doing E, from which you subtract the 5 doing all, the 4 doing E + H and the 2 doing M +E giving 8 just doing English.<BR>\n" );
document.write( "To summarise therefore<BR>\n" );
document.write( "M+E+H = 5<BR>\n" );
document.write( "M+E = 2<BR>\n" );
document.write( "M+H = 1<BR>\n" );
document.write( "E + H = 4<BR>\n" );
document.write( "M = 3<BR>\n" );
document.write( "E = 8<BR>\n" );
document.write( "H = 2<BR>\n" );
document.write( "which totals 25, so 3 are doing nothing. 3 are doing only M, and 3 + 2 + 8 = 13 are doing one subject.<BR>\n" );
document.write( "If you can transcribe these to a Venn diagram it will look clearer </SPAN>\n" );
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