document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=894461>Question 894461</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In how many ways we can arrange the letters in the word 'MISSISIPI' so that all S's come together and 2 I's come together .   the spelling of the word has been given like missisipi </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #542073 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=542073\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your original string of letters is missisipi.<BR>\n" );
document.write( "rearrange the terms so all the occurrences of s are together and all the occurrences of i are together.<BR>\n" );
document.write( "you will get miiiisssp.<BR>\n" );
document.write( "replace every 3 occcurrences of s with s and replace every 2 occurrences of i with i.<BR>\n" );
document.write( "you will get miisp<BR>\n" );
document.write( "the number of possible arrangements of miisp will be equal to 5! / 2! = (5*4*3*2*1) / (2*1) which becomes 5*4*3 which becomes 60.<BR>\n" );
document.write( "the number of possible arrangements of miisp will be equal to 60.<BR>\n" );
document.write( "that should beyour answer.<BR>\n" );
document.write( "there are 60 possible arrangements.\r<BR>\n" );
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document.write( "there are too many to go through to confirm, but we can use a simpler example to see if the formula is correct.\r<BR>\n" );
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document.write( "start with missisipi<BR>\n" );
document.write( "let's drop an s and drop a p.<BR>\n" );
document.write( "we are left with missiii<BR>\n" );
document.write( "we want to group all occurrences of s into one s and every pair of occurrences of i into one i.<BR>\n" );
document.write( "after we do that, we get:<BR>\n" );
document.write( "miis<BR>\n" );
document.write( "this is 4 characters and the number of possible arrangements will be 4! / 2! which is equal to 4*3 = 12<BR>\n" );
document.write( "this is a little bit more manageable so lets see what we get.\r<BR>\n" );
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document.write( "the 12 possible arrangements are:\r<BR>\n" );
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document.write( "iims<BR>\n" );
document.write( "iism<BR>\n" );
document.write( "imis<BR>\n" );
document.write( "imsi<BR>\n" );
document.write( "isim<BR>\n" );
document.write( "ismi<BR>\n" );
document.write( "miis<BR>\n" );
document.write( "misi<BR>\n" );
document.write( "msii<BR>\n" );
document.write( "siim<BR>\n" );
document.write( "simi<BR>\n" );
document.write( "smii\r<BR>\n" );
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document.write( "now we need to expand to see what we get:\r<BR>\n" );
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document.write( "we will replace every occurrence of s with ss and every occurrence of i with ii\r<BR>\n" );
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document.write( "we get:\r<BR>\n" );
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document.write( "iiiimss<BR>\n" );
document.write( "iiiissm<BR>\n" );
document.write( "iimiiss<BR>\n" );
document.write( "iimssii<BR>\n" );
document.write( "iissiim<BR>\n" );
document.write( "iissmii<BR>\n" );
document.write( "miiiiss<BR>\n" );
document.write( "miissii<BR>\n" );
document.write( "mssiiii<BR>\n" );
document.write( "ssiiiim<BR>\n" );
document.write( "ssiimii<BR>\n" );
document.write( "ssmiiii\r<BR>\n" );
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document.write( "every pair of occurrences of i are together and all occurrences of s are together so we have achieved what we want to achieve.\r<BR>\n" );
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document.write( "this confirms the formula is good and we can be reasonably confident it is correct when we apply it to the larger problem as we did on top.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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