document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1132437>Question 1132437</A>: <I><SPAN STYLE=\"word-break: break-all;\"> One hundred twenty people seated at different tables in a Mexican food restaurant were asked if their party had ordered any of the following items: enchiladas, chili con queso or quesadillas. 21 people had ordered none of these items; No one ordered only chili con queso; 5 ordered only quesadillas; 11 people had ordered all three of these items; 29 people had ordered chili con queso or quesadillas but did not order enchiladas; 79 people had ordered at least two of these items; 13 people had ordered enchiladas and quesadillas but had not ordered chili con queso; 26 people had ordered only enchiladas and chili con queso. <BR>\n" );
document.write( "What is the probability of choosing two persons that ordered only enchiladas? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #749477 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13214)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=749477\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The way I read the given information, it is inconsistent, making it impossible to solve the problem.<br><BR>\n" );
document.write( "We need to determine the number of people who ordered each combination of the 3 items, enchiladas (E), chili con queso (C), and quesadillas (Q).  The possible combinations are {none, E, C, Q, EC, EQ, CQ, EQC}.<br><BR>\n" );
document.write( "(1) 21 ordered none: none = 21<BR>\n" );
document.write( "(2) no one ordered only C: C = 0<BR>\n" );
document.write( "(3) 5 ordered only Q: Q = 5<BR>\n" );
document.write( "(4) 11 ordered all three: EQC = 11<BR>\n" );
document.write( "(5) 29 ordered C or Q but not E: C+Q+CQ = 0+5+CQ = 29 --> CQ = 24<BR>\n" );
document.write( "(6) 79 ordered either two or all three items: EC+EQ+CQ+EQC = 79 (we'll come back to this)<BR>\n" );
document.write( "(7) 13 ordered E and Q but not C: EQ = 13<BR>\n" );
document.write( "(8) 26 ordered only E and C: EC = 26<br><BR>\n" );
document.write( "Now going back to (6), we have EC+EQ+CQ+EQC = 79  -->  26+13+CQ+11 = 79  -->  CQ = 29<br><BR>\n" );
document.write( "But (5) says CQ is 24 and (8) says CQ is 29. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );