document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=658540>Question 658540</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the number of ways in which four letters of the word 'MATHEMATICS'can be arranged .answer is 2454 pls solve this\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 #410324 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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/cgi-bin/show-face.mpl?user=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=410324\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  I assume, for ordered combinations (i.e. permutations).\r<BR>\n" );
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document.write( "Removing the duplicate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M ALIGN=MIDDLE  ALT=\"M\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A ALIGN=MIDDLE  ALT=\"+A\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T ALIGN=MIDDLE  ALT=\"T\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" > different letters from which we can make \r<BR>\n" );
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document.write( "[8]P[4]=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+8%21%2F4%21=+1680 ALIGN=MIDDLE  ALT=\"+8%21%2F4%21=+1680\"   DISABLED_style= \"max-width:90%; height:auto;\" > permutations.\r<BR>\n" );
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document.write( "We need to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=add ALIGN=MIDDLE  ALT=\"add\"   DISABLED_style= \"max-width:90%; height:auto;\" > words having two <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M ALIGN=MIDDLE  ALT=\"M\"   DISABLED_style= \"max-width:90%; height:auto;\" >'s and two other distinct letters:\r<BR>\n" );
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document.write( "Pick two spots for the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M ALIGN=MIDDLE  ALT=\"M\"   DISABLED_style= \"max-width:90%; height:auto;\" >'s ([4]C[2] ways) and then assign the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7 ALIGN=MIDDLE  ALT=\"7\"   DISABLED_style= \"max-width:90%; height:auto;\" > other letters the two other spots ([7]P[2]). \r<BR>\n" );
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document.write( "So, we have ([4]C[2])([7]P[2]) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6+%2A+42+=+252 ALIGN=MIDDLE  ALT=\"6+%2A+42+=+252\"   DISABLED_style= \"max-width:90%; height:auto;\" > more possibilities.\r<BR>\n" );
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document.write( "We do the same for words with two <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A ALIGN=MIDDLE  ALT=\"A\"   DISABLED_style= \"max-width:90%; height:auto;\" >'s and those with two <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T ALIGN=MIDDLE  ALT=\"T\"   DISABLED_style= \"max-width:90%; height:auto;\" >'s, so we're now at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1680+%2B+3%2A252+=+2436 ALIGN=MIDDLE  ALT=\"1680+%2B+3%2A252+=+2436\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "We also need to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=add ALIGN=MIDDLE  ALT=\"add\"   DISABLED_style= \"max-width:90%; height:auto;\" > words having pairs of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=identical ALIGN=MIDDLE  ALT=\"identical\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+letters ALIGN=MIDDLE  ALT=\"+letters\"   DISABLED_style= \"max-width:90%; height:auto;\" > like MAMA and TAAT... \r<BR>\n" );
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document.write( "For two <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M ALIGN=MIDDLE  ALT=\"M\"   DISABLED_style= \"max-width:90%; height:auto;\" >'s and two <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A ALIGN=MIDDLE  ALT=\"A\"   DISABLED_style= \"max-width:90%; height:auto;\" >'s, there are [4]C[2]=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" > possibilities. Same for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M ALIGN=MIDDLE  ALT=\"M\"   DISABLED_style= \"max-width:90%; height:auto;\" >'s and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T ALIGN=MIDDLE  ALT=\"T\"   DISABLED_style= \"max-width:90%; height:auto;\" >'s, and same for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A ALIGN=MIDDLE  ALT=\"A\"   DISABLED_style= \"max-width:90%; height:auto;\" >'s and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T ALIGN=MIDDLE  ALT=\"T\"   DISABLED_style= \"max-width:90%; height:auto;\" >'s. <BR>\n" );
document.write( "This add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18 ALIGN=MIDDLE  ALT=\"18\"   DISABLED_style= \"max-width:90%; height:auto;\" > to our total.\r<BR>\n" );
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document.write( "so, we have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2436%2B18=2454 ALIGN=MIDDLE  ALT=\"2436%2B18=2454\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Answer: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2454 ALIGN=MIDDLE  ALT=\"2454\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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