document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=892937>Question 892937</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An exam paper in mathematics contains 12 questions and students must answer 10 of them.<BR>\n" );
document.write( "a) in how many ways can a student choose 10 out of the 12 questions to answer?<BR>\n" );
document.write( "b) show, by using the extended pigeonhole principle, that if 200 students write the exam paper, then at least 4 students will choose the same 10 questions to answer. state clearly what the pigeons and pigeonholes are. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #541214 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=541214\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a) 12C10 = 12C2 = 12*11/2! = 66 ways<BR>\n" );
document.write( "b) Assign each pigeon (student) to a pigeonhole (a subset of 10 questions to be answered). Since 200/66 > 3, there is a set of 10 questions that is answered by at least four students. </SPAN>\n" );
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