document.write( "Question 1183742: How many ways can the letters of the word MISSISSIPPI be arranged if no two S's are side by side? \n" ); document.write( "

Algebra.Com's Answer #814189 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "How many ways can the letters of the word MISSISSIPPI be arranged if no two S's are side by side?
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\n" ); document.write( "\n" ); document.write( "Since you use the term \"arranged\", I will assume that you know the difference between permutations and arrangements,
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document.write( "First, take off all letters S from the word. You will get\r\n" );
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document.write( "      MIIIPPI\r\n" );
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document.write( "Next, insert blanks between the remaining letters.  Also, place blanks before the first letter and after last letter.\r\n" );
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document.write( "You will get\r\n" );
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document.write( "    _M_I_I_I_P_P_I_\r\n" );
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document.write( "with 8 blanks.  \r\n" );
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document.write( "Now you have 7-letters word MIIIPPI with 4 repeating letter I  and 2 repeating letters P.\r\n" );
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document.write( "You can arrange them in   =  = 105 distinguishable ways.    (1)\r\n" );
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document.write( "Finally, you distribute four letters S, one after one, among 8 blank positions, placing one S into one blank.\r\n" );
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document.write( "You can do it by   =  = 70 ways.    (2)\r\n" );
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document.write( "Now, combining 105 arrangements (1) with 70 independent arrangements (2), you have 105*70 = 7350 total possible arrangements \r\n" );
document.write( "of the word MISSISSIPPI with no two S's side by side.\r\n" );
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