document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=167636>Question 167636</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a pick 6 lottery game, ten balls labeled zero through nine are placed ina jar and selected one at a time, without replacement. To win, you must match all six in any order. How many possible sets of six numbers are there? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #123527 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=123527\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Since order does not matter (the balls can be arranged in any order), we must use the <a  rel=nofollow HREF=http://www.mathwords.com/c/combination_formula.htm>combination formula</a>:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{n}C_{r}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%21%2F%28n-r%29%21r%21 ALIGN=MIDDLE  ALT=\"n%21%2F%28n-r%29%21r%21\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the combination formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{10}C_{6}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%21%2F%2810-6%29%216%21 ALIGN=MIDDLE  ALT=\"10%21%2F%2810-6%29%216%21\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=10 ALIGN=MIDDLE  ALT=\"n=10\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=6 ALIGN=MIDDLE  ALT=\"r=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{10}C_{6}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%21%2F4%216%21 ALIGN=MIDDLE  ALT=\"10%21%2F4%216%21\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10-6 ALIGN=MIDDLE  ALT=\"10-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get 4\r<BR>\n" );
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document.write( "Expand 10!<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{10}C_{6}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2810%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%2F4%216%21 ALIGN=MIDDLE  ALT=\"%2810%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%2F4%216%21\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Expand 4!<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{10}C_{6}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2810%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%2F%284%2A3%2A2%2A1%296%21 ALIGN=MIDDLE  ALT=\"%2810%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%2F%284%2A3%2A2%2A1%296%21\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{10}C_{6}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2810%2A9%2A8%2A7%2A6%2A5%2Across%284%2A3%2A2%2A1%29%29%2F%28cross%284%2A3%2A2%2A1%29%296%21 ALIGN=MIDDLE  ALT=\"%2810%2A9%2A8%2A7%2A6%2A5%2Across%284%2A3%2A2%2A1%29%29%2F%28cross%284%2A3%2A2%2A1%29%296%21\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Cancel\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{10}C_{6}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2810%2A9%2A8%2A7%2A6%2A5%29%2F6%21 ALIGN=MIDDLE  ALT=\"%2810%2A9%2A8%2A7%2A6%2A5%29%2F6%21\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Simplify\r<BR>\n" );
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document.write( "Expand 6!<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{10}C_{6}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2810%2A9%2A8%2A7%2A6%2A5%29%2F%286%2A5%2A4%2A3%2A2%2A1%29 ALIGN=MIDDLE  ALT=\"%2810%2A9%2A8%2A7%2A6%2A5%29%2F%286%2A5%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/rendertex.cgi?\LARGE \textrm{_{10}C_{6}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=151200%2F%286%2A5%2A4%2A3%2A2%2A1%29 ALIGN=MIDDLE  ALT=\"151200%2F%286%2A5%2A4%2A3%2A2%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Multiply 10*9*8*7*6*5 to get 151,200\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{10}C_{6}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=151200%2F720 ALIGN=MIDDLE  ALT=\"151200%2F720\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 6*5*4*3*2*1 to get 720\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{10}C_{6}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=210 ALIGN=MIDDLE  ALT=\"210\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide\r<BR>\n" );
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document.write( "So 10 choose 6 (where order doesn't matter) yields 210 unique combinations\r<BR>\n" );
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document.write( "So there are 210 possible ways to pick 6 numbers from a pool of 10 numbers. </SPAN>\n" );
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