document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1194633>Question 1194633</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 3.	Construct a table listing all possible samples of size 7<BR>\n" );
document.write( "Combination: 87, 92, 93, 93, 94, 94, 95, 96, 97<BR>\n" );
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document.write( "Must be 36 samples </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #826885 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3816)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=826885\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "As the other tutor mentioned, you can form subsets of size 7 by picking subsets of size 2. <BR>\n" );
document.write( "Whatever 2 items you pick, they will be ignored so you can focus on the other 7 items.\r<BR>\n" );
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document.write( "Because this value 2 shows up, it may be handy to form a two-way table. In this case, we'll have a 9 row and 9 column two-way table like this.<TABLE  border = \"1\" cellpadding = \"5\">\n" );
document.write( "<tr><TD ></TD><TD >87</TD><TD >92</TD><TD >93</TD><TD >93</TD><TD >94</TD><TD >94</TD><TD >95</TD><TD >96</TD><TD >97</TD></tr><tr><TD >87</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD></tr><tr><TD >92</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD></tr><tr><TD >93</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD></tr><tr><TD >93</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD></tr><tr><TD >94</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD></tr><tr><TD >94</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD></tr><tr><TD >95</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD></tr><tr><TD >96</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD></tr><tr><TD >97</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD></tr>\n" );
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document.write( "Write X's along the main diagonal. <BR>\n" );
document.write( "This is because we cannot select the same item twice when forming a 2 element subset.<BR>\n" );
document.write( "<TABLE  border = \"1\" cellpadding = \"5\">\n" );
document.write( "<tr><TD ></TD><TD >87</TD><TD >92</TD><TD >93</TD><TD >93</TD><TD >94</TD><TD >94</TD><TD >95</TD><TD >96</TD><TD >97</TD></tr><tr><TD >87</TD><TD >X</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD></tr><tr><TD >92</TD><TD ></TD><TD >X</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD></tr><tr><TD >93</TD><TD ></TD><TD ></TD><TD >X</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD></tr><tr><TD >93</TD><TD ></TD><TD ></TD><TD ></TD><TD >X</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD></tr><tr><TD >94</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD >X</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD></tr><tr><TD >94</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD >X</TD><TD ></TD><TD ></TD><TD ></TD></tr><tr><TD >95</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD >X</TD><TD ></TD><TD ></TD></tr><tr><TD >96</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD >X</TD><TD ></TD></tr><tr><TD >97</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD >X</TD></tr>\n" );
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document.write( "We'll also write X's in every entry below the diagonal. <BR>\n" );
document.write( "Why? Notice that stuff below the diagonal mirrors the stuff above the diagonal.<BR>\n" );
document.write( "Example: look at row 2, column 1 and you'll see we're dealing with the same values as row 1, column 2. Both of those values being 87 and 92 in either order.<BR>\n" );
document.write( "<TABLE  border = \"1\" cellpadding = \"5\">\n" );
document.write( "<tr><TD ></TD><TD >87</TD><TD >92</TD><TD >93</TD><TD >93</TD><TD >94</TD><TD >94</TD><TD >95</TD><TD >96</TD><TD >97</TD></tr><tr><TD >87</TD><TD >X</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD></tr><tr><TD >92</TD><TD >X</TD><TD >X</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD></tr><tr><TD >93</TD><TD >X</TD><TD >X</TD><TD >X</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD></tr><tr><TD >93</TD><TD >X</TD><TD >X</TD><TD >X</TD><TD >X</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD></tr><tr><TD >94</TD><TD >X</TD><TD >X</TD><TD >X</TD><TD >X</TD><TD >X</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD></tr><tr><TD >94</TD><TD >X</TD><TD >X</TD><TD >X</TD><TD >X</TD><TD >X</TD><TD >X</TD><TD ></TD><TD ></TD><TD ></TD></tr><tr><TD >95</TD><TD >X</TD><TD >X</TD><TD >X</TD><TD >X</TD><TD >X</TD><TD >X</TD><TD >X</TD><TD ></TD><TD ></TD></tr><tr><TD >96</TD><TD >X</TD><TD >X</TD><TD >X</TD><TD >X</TD><TD >X</TD><TD >X</TD><TD >X</TD><TD >X</TD><TD ></TD></tr><tr><TD >97</TD><TD >X</TD><TD >X</TD><TD >X</TD><TD >X</TD><TD >X</TD><TD >X</TD><TD >X</TD><TD >X</TD><TD >X</TD></tr>\n" );
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document.write( "The empty cells that haven't been crossed out are then filled with the 7 element subsets<BR>\n" );
document.write( "For example, in row 1, column 2 we'll have the subset {93, 93, 94, 94, 95, 96, 97} which is everything except the 87 & 92<BR>\n" );
document.write( "<TABLE  border = \"1\" cellpadding = \"5\">\n" );
document.write( "<tr><TD ></TD><TD >87</TD><TD >92</TD><TD >93</TD><TD >93</TD><TD >94</TD><TD >94</TD><TD >95</TD><TD >96</TD><TD >97</TD></tr><tr><TD >87</TD><TD >X</TD><TD ><font size=2>{93, 93, 94, 94, 95, 96, 97}</font></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD></tr><tr><TD >92</TD><TD >X</TD><TD >X</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD></tr><tr><TD >93</TD><TD >X</TD><TD >X</TD><TD >X</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD></tr><tr><TD >93</TD><TD >X</TD><TD >X</TD><TD >X</TD><TD >X</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD></tr><tr><TD >94</TD><TD >X</TD><TD >X</TD><TD >X</TD><TD >X</TD><TD >X</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD></tr><tr><TD >94</TD><TD >X</TD><TD >X</TD><TD >X</TD><TD >X</TD><TD >X</TD><TD >X</TD><TD ></TD><TD ></TD><TD ></TD></tr><tr><TD >95</TD><TD >X</TD><TD >X</TD><TD >X</TD><TD >X</TD><TD >X</TD><TD >X</TD><TD >X</TD><TD ></TD><TD ></TD></tr><tr><TD >96</TD><TD >X</TD><TD >X</TD><TD >X</TD><TD >X</TD><TD >X</TD><TD >X</TD><TD >X</TD><TD >X</TD><TD ></TD></tr><tr><TD >97</TD><TD >X</TD><TD >X</TD><TD >X</TD><TD >X</TD><TD >X</TD><TD >X</TD><TD >X</TD><TD >X</TD><TD >X</TD></tr>\n" );
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document.write( "I'll let you fill out the rest.\r<BR>\n" );
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document.write( "Edit: I realize that there are duplicate entries (93 and 94). I'm not sure if your teacher made a typo or not. I'll keep my answer as is, since it may be useful for similar types of problems of this nature.<BR>\n" );
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