document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=94351>Question 94351</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the number of permutations of the first 8 letters of the alphabet for each situation.     taking 3 letters at a time </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #68679 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=68679\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Since order does matter (this is because the word \"cab\" is different than \"abc\"), we can use the <a  rel=nofollow HREF=http://www.mathwords.com/p/permutation_formula.htm>permutation formula</a>:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{n}P_{r}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%21%2F%28n-r%29%21 ALIGN=MIDDLE  ALT=\"n%21%2F%28n-r%29%21\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given formula\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{8}P_{3}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%21%2F%288-3%29%21 ALIGN=MIDDLE  ALT=\"8%21%2F%288-3%29%21\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=8 ALIGN=MIDDLE  ALT=\"n=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > (this is number of letters given) and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=3 ALIGN=MIDDLE  ALT=\"r=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > (this is the number of letters we can use together at a time)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{8}P_{3}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%21%2F5%21 ALIGN=MIDDLE  ALT=\"8%21%2F5%21\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8-3 ALIGN=MIDDLE  ALT=\"8-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get 5\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Expand 8!<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{8}P_{3}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%2F5%21 ALIGN=MIDDLE  ALT=\"%288%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%2F5%21\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Expand 5!<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{8}P_{3}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%2F%285%2A4%2A3%2A2%2A1%29 ALIGN=MIDDLE  ALT=\"%288%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%2F%285%2A4%2A3%2A2%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{8}P_{3}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288%2A7%2A6%2Across%285%2A4%2A3%2A2%2A1%29%29%2F%28cross%285%2A4%2A3%2A2%2A1%29%29 ALIGN=MIDDLE  ALT=\"%288%2A7%2A6%2Across%285%2A4%2A3%2A2%2A1%29%29%2F%28cross%285%2A4%2A3%2A2%2A1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Cancel\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{8}P_{3}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2A7%2A6 ALIGN=MIDDLE  ALT=\"8%2A7%2A6\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Simplify\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{8}P_{3}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=336 ALIGN=MIDDLE  ALT=\"336\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Now multiply 8*7*6 to get 336\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So 8 choose 3 (where order does matter) yields 336 unique combinations\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );