document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1072879>Question 1072879</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A container contains 10 diesel engines. The company chooses 6 engines at&#8203; random, and will not ship the container if any of the engines chosen are defective. Find the probability that a container will be shipped even though it contains 2 defectives if the sample size is 6.\r<BR>\n" );
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document.write( "Can someone please breakdown the steps to solve this. This is an online class and the help feature isn't explaining how to get the numbers needed to solve it. Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #687735 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=687735\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I am baffled by the phrase \"if the sample size is 6\" at the end of the problem.<BR>\n" );
document.write( "The problem said before that the company chooses 6 engines out of the 10 in the container. What is that phrase about sample size for?<BR>\n" );
document.write( " <BR>\n" );
document.write( "Anyway, there are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C1%2C10%2C6%29%29=%28matrix%282%2C1%2C10%2C4%29%29=10%2A9%2A8%2A7%2F%284%2A3%2A2%29=10%2A3%2A7=210 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "different possible sets of 6 engines that can be chosen.<BR>\n" );
document.write( "NOTE: That is combinations of 10 taking 6 at a time.<BR>\n" );
document.write( "Your online class may use a symbol with a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C ALIGN=MIDDLE  ALT=\"C\"   DISABLED_style= \"max-width:90%; height:auto;\" > for combinations,<BR>\n" );
document.write( "instead of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C1%2C10%2C6%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%282%2C1%2C10%2C6%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > notation I used.<BR>\n" );
document.write( " <BR>\n" );
document.write( "There are only <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C1%2C8%2C6%29%29=%28matrix%282%2C1%2C8%2C2%29%29=8%2A7%2F2=4%2A7=28 ALIGN=MIDDLE  ALT=\"%28matrix%282%2C1%2C8%2C6%29%29=%28matrix%282%2C1%2C8%2C2%29%29=8%2A7%2F2=4%2A7=28\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "sets of 6 good engines that can be made with the<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10-2=8 ALIGN=MIDDLE  ALT=\"10-2=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > good engines in that container that has <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > defective ones.<BR>\n" );
document.write( "As a fraction that is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=28%2F210=highlight%282%2F15%29 ALIGN=MIDDLE  ALT=\"28%2F210=highlight%282%2F15%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and that is the probability that the set of 6 engines chosen does not have a defective one.<BR>\n" );
document.write( " <BR>\n" );
document.write( "FORMULAS:<BR>\n" );
document.write( "I do not like formulas as a substitute for understanding concepts.<BR>\n" );
document.write( "The concept that is relevant to this problem is the concept of combinations.<BR>\n" );
document.write( "The number ways of choosing a set of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" > engines<BR>\n" );
document.write( "out of a set of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10 ALIGN=MIDDLE  ALT=\"10\"   DISABLED_style= \"max-width:90%; height:auto;\" > engines, can be seen as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C1%2C10%2C6%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%282%2C1%2C10%2C6%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > , the number of ways to pick the chosen <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C1%2C10%2C4%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%282%2C1%2C10%2C4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > , the number of ways of selecting the (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > not chosen.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C1%2C10%2C4%29%29=10%2A9%2A8%2A7%2F%284%2A3%2A2%29=10%2A3%2A7=210 ALIGN=MIDDLE  ALT=\"%28matrix%282%2C1%2C10%2C4%29%29=10%2A9%2A8%2A7%2F%284%2A3%2A2%29=10%2A3%2A7=210\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > factors in numerator, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > factors in denominator,<BR>\n" );
document.write( "makes for an easier calculation than<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C1%2C10%2C6%29%29=10%2A9%2A8%2A7%2A6%2A5%2F%286%2A5%2A4%2A3%2A2%29 ALIGN=MIDDLE  ALT=\"%28matrix%282%2C1%2C10%2C6%29%29=10%2A9%2A8%2A7%2A6%2A5%2F%286%2A5%2A4%2A3%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Below are the formulas and why they are the way they are.<BR>\n" );
document.write( " <BR>\n" );
document.write( "Permutations of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" > items taking all <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" > is<BR>\n" );
document.write( "the number of different ordered lists of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" > items that can be made <BR>\n" );
document.write( "from all <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" > items of a set of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" > different items is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=factorial ALIGN=MIDDLE  ALT=\"factorial\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22=%22 ALIGN=MIDDLE  ALT=\"%22=%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28k%21=k%2A%28k-1%29%2A%28k-2%29%2A%22...%22%2A3%2A2%2A1%29 ALIGN=MIDDLE  ALT=\"highlight%28k%21=k%2A%28k-1%29%2A%28k-2%29%2A%22...%22%2A3%2A2%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "because there are<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" > ways to pick the first item for the list,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28k-1%29 ALIGN=MIDDLE  ALT=\"%28k-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ways to pick the second item for the list,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28k-2%29 ALIGN=MIDDLE  ALT=\"%28k-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ways to pick the third item for the list,<BR>\n" );
document.write( "and so on, until you have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > ways to pick one of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > items not picked before,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ways to pick one of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > items not picked before,<BR>\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > choice for the last item on the list.<BR>\n" );
document.write( "That <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%21 ALIGN=MIDDLE  ALT=\"k%21\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the number of options a teacher would have<BR>\n" );
document.write( "to randomly line up all <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" > students in a class.<BR>\n" );
document.write( " <BR>\n" );
document.write( "Permutations of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > items taking <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" > of them is<BR>\n" );
document.write( "the number of different ordered lists of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" > items that can be made <BR>\n" );
document.write( "from the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > different items in a set.<BR>\n" );
document.write( "That number is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28n%21%2F%28n-k%29%21=n%2A%28n-1%29%2A%28n-2%29%2A%22...%22%2A%28n-k%2B3%29%2A%28n-k%2B2%29%2A%28n-k%2B1%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That is a product of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" > factors.<BR>\n" );
document.write( "That is the number of options a teacher would have to randomly select<BR>\n" );
document.write( "a line of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > students in the school.<BR>\n" );
document.write( "The teacher would have <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > choices for the first student in the line,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n-1%29 ALIGN=MIDDLE  ALT=\"%28n-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > choices for the second student in the line,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n-2%29 ALIGN=MIDDLE  ALT=\"%28n-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > choices for the third student in the line,<BR>\n" );
document.write( "and so on, until there are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n-k%2B1%29 ALIGN=MIDDLE  ALT=\"%28n-k%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > choices possible<BR>\n" );
document.write( "for the last of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" > picks.<BR>\n" );
document.write( "For the last of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" > picks,<BR>\n" );
document.write( "there are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n-k%2B1%29 ALIGN=MIDDLE  ALT=\"%28n-k%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > students wishing (or dreading) to be the last pick.<BR>\n" );
document.write( "(After that last pick, there are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n-k%29 ALIGN=MIDDLE  ALT=\"%28n-k%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > students left out,<BR>\n" );
document.write( "disappointed, or relieved that they were not picked).<BR>\n" );
document.write( "You can see how factors in the factorials ratio simplify leaving only <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" > factors.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%21%2F%28n-k%29%21=n%2A%28n-1%29%2A%28n-2%29%2A%22...%22%2A%28n-k%2B3%29%2A%28n-k%2B2%29%2A%28n-k%2B1%29%2A%28n-k%29%2A%28n-k-1%29%2A%22...%22%2A3%2A2%2A1%2F%28%28n-k%29%2A%28n-k-1%29%2A%22...%22%2A3%2A2%2A1%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "Combinations of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > items taking <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" > of them is<BR>\n" );
document.write( "the number of different sets of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" > items that can be made <BR>\n" );
document.write( "from the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > different items in a set.<BR>\n" );
document.write( "The formula for combinations of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > taken <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" > at a time is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%28matrix%282%2C1%2Cn%2Ck%29%29=n%21%2F%28k%21%28n-k%29%21%29=n%2A%28n-1%29%2A%22...%22%2A%28n-k%2B1%29%2F%28k%2A%28k-1%29%2A%22...%22%2A3%2A2%2A1%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "It is the number of possible sets <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > students in the school that can be made.<BR>\n" );
document.write( "There are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%21%2F%28n-k%29%21 ALIGN=MIDDLE  ALT=\"n%21%2F%28n-k%29%21\"   DISABLED_style= \"max-width:90%; height:auto;\" > possible lists,<BR>\n" );
document.write( "but they are not going to be lined up, order does not matter.<BR>\n" );
document.write( "Any <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > set of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" > students will be listed in a different order in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%21 ALIGN=MIDDLE  ALT=\"k%21\"   DISABLED_style= \"max-width:90%; height:auto;\" > lists,<BR>\n" );
document.write( "but it is just <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > set,<BR>\n" );
document.write( "so the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%21%2F%28n-k%29%21 ALIGN=MIDDLE  ALT=\"n%21%2F%28n-k%29%21\"   DISABLED_style= \"max-width:90%; height:auto;\" > possible lists boil doen to<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%21%2F%28%28n-k%29%21k%21%29 ALIGN=MIDDLE  ALT=\"n%21%2F%28%28n-k%29%21k%21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > possible sets. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );