document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=453172>Question 453172</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a class of 25, How many ways can a group of five students be selected? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #311383 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=311383\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "Since order does not matter, 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 given formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{25}C_{5}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25%21%2F%2825-5%29%215%21 ALIGN=MIDDLE  ALT=\"25%21%2F%2825-5%29%215%21\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=25 ALIGN=MIDDLE  ALT=\"n=25\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=5 ALIGN=MIDDLE  ALT=\"r=5\"   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{_{25}C_{5}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25%21%2F20%215%21 ALIGN=MIDDLE  ALT=\"25%21%2F20%215%21\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25-5 ALIGN=MIDDLE  ALT=\"25-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get 20\r<BR>\n" );
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document.write( "Expand 25!<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{25}C_{5}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2825%2A24%2A23%2A22%2A21%2A20%2A19%2A18%2A17%2A16%2A15%2A14%2A13%2A12%2A11%2A10%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%2F20%215%21 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Expand 20!<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{25}C_{5}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2825%2A24%2A23%2A22%2A21%2A20%2A19%2A18%2A17%2A16%2A15%2A14%2A13%2A12%2A11%2A10%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%2F%2820%2A19%2A18%2A17%2A16%2A15%2A14%2A13%2A12%2A11%2A10%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%295%21 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/rendertex.cgi?\LARGE \textrm{_{25}C_{5}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2825%2A24%2A23%2A22%2A21%2Across%2820%2A19%2A18%2A17%2A16%2A15%2A14%2A13%2A12%2A11%2A10%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%29%2F%28cross%2820%2A19%2A18%2A17%2A16%2A15%2A14%2A13%2A12%2A11%2A10%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%295%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{_{25}C_{5}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2825%2A24%2A23%2A22%2A21%29%2F5%21 ALIGN=MIDDLE  ALT=\"%2825%2A24%2A23%2A22%2A21%29%2F5%21\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Simplify\r<BR>\n" );
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document.write( "Expand 5!<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{25}C_{5}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2825%2A24%2A23%2A22%2A21%29%2F%285%2A4%2A3%2A2%2A1%29 ALIGN=MIDDLE  ALT=\"%2825%2A24%2A23%2A22%2A21%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/rendertex.cgi?\LARGE \textrm{_{25}C_{5}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6375600%2F%285%2A4%2A3%2A2%2A1%29 ALIGN=MIDDLE  ALT=\"6375600%2F%285%2A4%2A3%2A2%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Multiply 25*24*23*22*21 to get 6,375,600\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{25}C_{5}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6375600%2F120 ALIGN=MIDDLE  ALT=\"6375600%2F120\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 5*4*3*2*1 to get 120\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{25}C_{5}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=53130 ALIGN=MIDDLE  ALT=\"53130\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now divide\r<BR>\n" );
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document.write( "So 25 choose 5 (where order doesn't matter) yields 53,130 unique combinations\r<BR>\n" );
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document.write( "So there are 53,130 different ways to form a group of 5 people. <BR>\n" );
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