document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=849368>Question 849368</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how many distinct permutations can be made from the letters of the word \"mathematics\".  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #511534 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=511534\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the word mathematics has:\r<BR>\n" );
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document.write( "11 letters in total<BR>\n" );
document.write( "2 of the letter 'a'<BR>\n" );
document.write( "2 of the letter 'm'<BR>\n" );
document.write( "2 of the letter 't'\r<BR>\n" );
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document.write( "i believe that's all the duplicates.\r<BR>\n" );
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document.write( "the permutation formula is 11! / (2! * 2! * 2!)\r<BR>\n" );
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document.write( "this becomes 11! / 8 which is equal to 4,989,600.\r<BR>\n" );
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document.write( "you take the permutation of the whole number and you divide by the permutation of each of the duplicates.\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "consider the letters ABC.\r<BR>\n" );
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document.write( "the permutation of these is 3! = 6.\r<BR>\n" );
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document.write( "those permutations are:\r<BR>\n" );
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document.write( "ABC<BR>\n" );
document.write( "ACB<BR>\n" );
document.write( "BAC<BR>\n" );
document.write( "BCA<BR>\n" );
document.write( "CAB<BR>\n" );
document.write( "CBA\r<BR>\n" );
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document.write( "now consider the permutation of the letters AAC.\r<BR>\n" );
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document.write( "use the formula given above and you get 3! / 2! which is equal to 6/2 = 3.\r<BR>\n" );
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document.write( "those permutations are:\r<BR>\n" );
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document.write( "AAC<BR>\n" );
document.write( "ACA<BR>\n" );
document.write( "CAA\r<BR>\n" );
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document.write( "                  </SPAN>\n" );
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