document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=199877>Question 199877</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This is the last problem that i missed on my exam please help me .. so I will have it straigh for my final.  thank you T-Aun\r<BR>\n" );
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document.write( "How many different ways are there for an admissions officer to select a group of 6 college candidates from a group of 15 applicants for an interview? \r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #150245 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=150245\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Unfortunately, the previous solution is incorrect. Why? They're not looking for a probability, they just want to know the number of possible combinations.\r<BR>\n" );
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document.write( "We could use the counting principle to solve this problem, but we'll have overlap and the sample space is far too large. So let's do it this way:\r<BR>\n" );
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document.write( "In this case, order does NOT matter since the candidates have no rank over one another (ie one isn't president or secretary). \r<BR>\n" );
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document.write( "Since order does not matter, we must use the &lt;a  rel=nofollow HREF=http://www.mathwords.com/c/combination_formula.htm&gt;combination formula&lt;/a&gt;:\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{_{15}C_{6}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%21%2F%2815-6%29%216%21 ALIGN=MIDDLE  ALT=\"15%21%2F%2815-6%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=15 ALIGN=MIDDLE  ALT=\"n=15\"   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{_{15}C_{6}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%21%2F9%216%21 ALIGN=MIDDLE  ALT=\"15%21%2F9%216%21\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15-6 ALIGN=MIDDLE  ALT=\"15-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get 9\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{15}C_{6}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2815%2A14%2A13%2A12%2A11%2A10%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%2F9%216%21 ALIGN=MIDDLE  ALT=\"%2815%2A14%2A13%2A12%2A11%2A10%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%2F9%216%21\"   DISABLED_style= \"max-width:90%; height:auto;\" > Expand 15!\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{15}C_{6}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2815%2A14%2A13%2A12%2A11%2A10%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%2F%289%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%296%21 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Expand 9!\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{15}C_{6}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2815%2A14%2A13%2A12%2A11%2A10%2Across%289%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%29%2F%28cross%289%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%296%21 ALIGN=MIDDLE   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{_{15}C_{6}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2815%2A14%2A13%2A12%2A11%2A10%29%2F6%21 ALIGN=MIDDLE  ALT=\"%2815%2A14%2A13%2A12%2A11%2A10%29%2F6%21\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{15}C_{6}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2815%2A14%2A13%2A12%2A11%2A10%29%2F%286%2A5%2A4%2A3%2A2%2A1%29 ALIGN=MIDDLE  ALT=\"%2815%2A14%2A13%2A12%2A11%2A10%29%2F%286%2A5%2A4%2A3%2A2%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Expand 6!\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{15}C_{6}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3603600%2F%286%2A5%2A4%2A3%2A2%2A1%29 ALIGN=MIDDLE  ALT=\"3603600%2F%286%2A5%2A4%2A3%2A2%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Multiply 15*14*13*12*11*10 to get 3,603,600\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{15}C_{6}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3603600%2F720 ALIGN=MIDDLE  ALT=\"3603600%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{_{15}C_{6}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5005 ALIGN=MIDDLE  ALT=\"5005\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce.\r<BR>\n" );
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document.write( "So 15 choose 6 (where order doesn't matter) yields 5,005 unique combinations\r<BR>\n" );
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document.write( "This means that there are 5,005  different ways to select a group of 6 college candidates from a group of 15 applicants for an interview (where the order of the candidates doesn't matter).\r<BR>\n" );
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