document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1066088>Question 1066088</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a 10-item Mathematics problem-solving test, how many ways can you select 5 problems to solve? How many ways can you select the 5 questions if you are required to answer question number 10?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #681467 by </B><A HREF=/tutors/aboutme.mpl?userid=swincher4391><B>swincher4391(1107)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=swincher4391><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=swincher4391><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=681467\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Part a)\r<BR>\n" );
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document.write( "Since it appears that the order does not matter (we are just choosing any 5 at once), then we are using a combination. A couple of different ways to compute this.\r<BR>\n" );
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document.write( "You can use the nCr button on your calculator, but I will do it using the formula.\r<BR>\n" );
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document.write( "So  nCr  = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%21%2F%28%28n-r%29%21%2A+r%21%29 ALIGN=MIDDLE  ALT=\"n%21%2F%28%28n-r%29%21%2A+r%21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We are finding 10 C 5 =   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+10%21+%2F%285%21+%2A+5%21%29+ ALIGN=MIDDLE  ALT=\"+10%21+%2F%285%21+%2A+5%21%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "10! is quite large, so let's try to do some simplification.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2810%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%2F%28%285%2A4%2A3%2A2%2A1%29%2A%285%2A4%2A3%2A2%2A1%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2810%2A9%2A8%2A7%2A6%2Across%285%29%2Across%284%29%2Across%283%29%2Across%282%29%2Across%281%29%29%2F%28%28cross%285%29%2Across%284%29%2Across%283%29%2Across%282%29%2Across%281%29%29%2A%285%2A4%2A3%2A2%2A1%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2810%2A9%2A8%2A7%2A6%29%2F%285%2A4%2A3%2A2%2A1%29 ALIGN=MIDDLE  ALT=\"%2810%2A9%2A8%2A7%2A6%29%2F%285%2A4%2A3%2A2%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28cross%2810%29%2A9%2A8%2A7%2A6%29%2F%28cross%285%29%2A4%2A3%2Across%282%29%2A1%29 ALIGN=MIDDLE  ALT=\"%28cross%2810%29%2A9%2A8%2A7%2A6%29%2F%28cross%285%29%2A4%2A3%2Across%282%29%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289%2A8%2A7%2A6%29%2F%284%2A3%29 ALIGN=MIDDLE  ALT=\"%289%2A8%2A7%2A6%29%2F%284%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28cross%289%293%2Across%288%292%2A7%2A6%29%2F%28cross%284%29%2Across%283%29%29 ALIGN=MIDDLE  ALT=\"%28cross%289%293%2Across%288%292%2A7%2A6%29%2F%28cross%284%29%2Across%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and 3 * 2* 7 * 6  is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28252%29 ALIGN=MIDDLE  ALT=\"highlight%28252%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Part b)\r<BR>\n" );
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document.write( "10 is fixed so we really only have  9 questions and we are choosing 4.\r<BR>\n" );
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document.write( "So  9 C 4 = \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%2F%28%285%2A4%2A3%2A2%2A1%29%284%2A3%2A2%2A1%29%29 ALIGN=MIDDLE  ALT=\"%289%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%2F%28%285%2A4%2A3%2A2%2A1%29%284%2A3%2A2%2A1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289%2A8%2A7%2A6%29%2F%284%2A3%2A2%2A1%29 ALIGN=MIDDLE  ALT=\"%289%2A8%2A7%2A6%29%2F%284%2A3%2A2%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28cross%289%293%2Across%288%29%2A7%2A6%29%2F%28cross%284%29%2Across%283%29%2Across%282%29%2Across%281%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So 3 * 7 * 6 =  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28126%29 ALIGN=MIDDLE  ALT=\"highlight%28126%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "------------------------------------<BR>\n" );
document.write( "Finally, Google will do it for you as well.\r<BR>\n" );
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document.write( "10 choose 5 : https://www.google.com/#q=10+choose+5\r<BR>\n" );
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document.write( "9 choose 4 : https://www.google.com/#q=9+choose+4<BR>\n" );
document.write( " </SPAN>\n" );
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