document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=480557>Question 480557</A>: <I><SPAN STYLE=\"word-break: break-all;\"> HOW MANY PERMUTATIONS ARE THERE OF THE FOLLOWING WORD.<BR>\n" );
document.write( "M n1                       MATHEMATICS    11 LETTERS    n=11<BR>\n" );
document.write( "A n2<BR>\n" );
document.write( "T n3<BR>\n" );
document.write( "H n4 <BR>\n" );
document.write( "E n5<BR>\n" );
document.write( "M n6           ( 11              )    11!<BR>\n" );
document.write( "C n7                                 _____<BR>\n" );
document.write( "T n8           ( 2,2,2,1,1,1,1,1 )= 2!2!2!1!1!1!1!1!  now the question is what <BR>\n" );
document.write( "I n9                                                  do I do after this? <BR>\n" );
document.write( "C n10                                                 PLEASE SOMEONE EXPLAIN TO <BR>\n" );
document.write( "S n11                                                 ME STEP BY STEP:: THANKS   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #329115 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=329115\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> mathematics has 11 letters.<BR>\n" );
document.write( "there are 2 m's<BR>\n" );
document.write( "there are 2 a's<BR>\n" );
document.write( "that are 2 t's<BR>\n" );
document.write( "the number of permutations should be:<BR>\n" );
document.write( "11! / (2!*2!*2!) = 4989600<BR>\n" );
document.write( "to see how this works, use much smaller numbers.<BR>\n" );
document.write( "suppose your letters were \"mat\"<BR>\n" );
document.write( "the number of permutations would be 3! = 6<BR>\n" );
document.write( "those permutations would be:<BR>\n" );
document.write( "mat<BR>\n" );
document.write( "mta<BR>\n" );
document.write( "amt<BR>\n" );
document.write( "atm<BR>\n" );
document.write( "tam<BR>\n" );
document.write( "tma<BR>\n" );
document.write( "now suppose your letters were \"mma\"<BR>\n" );
document.write( "the number of permutations would be 3!/2! because 2 of the letters were the same.<BR>\n" );
document.write( "those permutations would be:<BR>\n" );
document.write( "mma<BR>\n" );
document.write( "mam<BR>\n" );
document.write( "amm<BR>\n" );
document.write( "now suppose your letters were \"mmat\"<BR>\n" );
document.write( "the number of permutations, if our equation is correct, would be 4!/2! = 12<BR>\n" );
document.write( "those permutations would be:<BR>\n" );
document.write( "mmat<BR>\n" );
document.write( "mmta\r<BR>\n" );
document.write( "\n" );
document.write( "mamt<BR>\n" );
document.write( "matm<BR>\n" );
document.write( "ammt<BR>\n" );
document.write( "amtm\r<BR>\n" );
document.write( "\n" );
document.write( "mtam<BR>\n" );
document.write( "mtma<BR>\n" );
document.write( "tmam<BR>\n" );
document.write( "tmma\r<BR>\n" );
document.write( "\n" );
document.write( "atmm<BR>\n" );
document.write( "tamm\r<BR>\n" );
document.write( "\n" );
document.write( "that's a total of 12.\r<BR>\n" );
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document.write( "now, suppose your letters are \"mmtt\"\r<BR>\n" );
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document.write( "the number of permutations would be 4!/(2!*2!) = 24/4 = 6\r<BR>\n" );
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document.write( "those permutations would be:\r<BR>\n" );
document.write( "\n" );
document.write( "mmtt<BR>\n" );
document.write( "ttmm\r<BR>\n" );
document.write( "\n" );
document.write( "mtmt<BR>\n" );
document.write( "tmtm\r<BR>\n" );
document.write( "\n" );
document.write( "tmmt<BR>\n" );
document.write( "mttm\r<BR>\n" );
document.write( "\n" );
document.write( "that's a total of 6.<BR>\n" );
document.write( "the formula works as can be seen with the smaller numbers.<BR>\n" );
document.write( "applying it to the larger numbers gets you<BR>\n" );
document.write( "number of permutations in \"mathematics\" is equal to 11!/(2!*2!*2!) = 4989600.\r<BR>\n" );
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document.write( "11! / (2!*2!*2!) is equal to 11*10*9*8*7*6*5*4*3*2*1 / 2*1*2*1*2*1<BR>\n" );
document.write( "since the denominator winds up being 8, we cancel the 8 from the numerator with it to get:<BR>\n" );
document.write( "11! / (2!*2!*2!) = 11*10*9*7*6*5*4*3*2*1<BR>\n" );
document.write( "this is equivalent to:<BR>\n" );
document.write( "11! / (2!2!*2!) = 110 * 96 * 30 * 12 * 2 which is equal to 6930 * 720 which is equal to 4989600\r<BR>\n" );
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document.write( "formula looks good and that should be your answer.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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