document.write( "Question 1205807: How many four - letter code words are possible using the letters in PONTIAN if the letters are chosen with replacement, but any two \" N\" cannot appear together?
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Algebra.Com's Answer #842845 by ikleyn(52790) $\"\"$ $\"About$

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document.write( "In the word PONTIAN, where are 7 letters, in all; of them, letter N repeats twice;\r\n" );
document.write( "other letters are unique.\r\n" );
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document.write( "Consider three cases, sequentially.\r\n" );
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document.write( "Case 1.  There is no \"N\" in a four-letter code.\r\n" );
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document.write( "         Then there are 5 different letters to use, (P, O, T, I, A) \r\n" );
document.write( "         and we can use any of these 5 letters in each of 4 positions.\r\n" );
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document.write( "         In all, there are  = 625 such 4-letter codes.\r\n" );
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document.write( "Case 2.  There is only one letter \"N\" in a four-letter code.\r\n" );
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document.write( "         Then there are 6 different letters to use, (P, O, T, I, A, N).\r\n" );
document.write( "         We place \"N\" in any of 4 positions, and we can use any of 5 remaining letters \r\n" );
document.write( "         in the remaining 3 positions.\r\n" );
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document.write( "         It gives us  = 500 such 4-letter codes.\r\n" );
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document.write( "Case 3.  There are two letters \"N\" in a four-letter code, but these two \"N\" can not appear together.\r\n" );
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document.write( "         Then for these two \"N\" we have  - 3 =  = 2*3-3 = 6-3 = 3 possible places/locations \r\n" );
document.write( "         in the row of 4 positions.  (Here minus 3 means excluding cases when two \"N\" appears together).\r\n" );
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document.write( "         In two remaining positions, we can place any of 5 remaining letters.\r\n" );
document.write( "         it gives the factor  = 25.\r\n" );
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document.write( "         In all, there are 4*25 = 100 such 4-letter codes.\r\n" );
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document.write( "Now, to get the answer, we should add 625 + 500 + 100 = 1225  possible 4-letter codes.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Do not write the term \"four-letter code\" as \"four - letter code\".\r
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\n" ); document.write( "\n" ); document.write( "Write it in correct form as \"four-letter code\".\r
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