document.write( "Question 1202209: A password must be created using 4 letters from the word \"PASSWORD\". In how many ways can the letter be arranged?
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Algebra.Com's Answer #836884 by ikleyn(52794) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "A password must be created using 4 letters from the word \"PASSWORD\".
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document.write( "In this word \"PASSWORD\", there are 7 different letters; one letter \"S\" is repeated twice.\r\n" );
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document.write( "Let's consider first the case, when all 4 letters of a password are different.\r\n" );
document.write( "There are  7*6*5*4 = 840 such passwords (arranging).\r\n" );
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document.write( "Now consider the opposite case, when two letters in password are \"S\".\r\n" );
document.write( "There are   =  = 3*5 = 15 ways to select the remaining \r\n" );
document.write( "two letters from 6 = 8-2 letters, different from \"S\".\r\n" );
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document.write( "Further, this number 15 we should multiply by the number of different arranging of 4 letters,\r\n" );
document.write( "two of which are identical \"S\".\r\n" );
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document.write( "So the number of these passwords with two \"S\" is   = 15*12 = 180.\r\n" );
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document.write( "In all, we have the number of all possible distinguishable passwords/arranging  840 + 180 = 1020.    ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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My note to note by @greenestamps

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\n" ); document.write( "\n" ); document.write( "In his post-solution note, tutor @greenestamps writes\r
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document.write( "    NOTE: The solution shown by tutor @ikleyn is very likely the question that the problem INTENDED to ask.\r\n" );
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document.write( "    However, the wording of the problem implies that 4 letters are chosen from the letters in PASSWORD; and then THOSE 4 LETTERS are arranged.\r\n" );
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\n" ); document.write( "\n" ); document.write( "      The wording of the problem DOES NOT implies that 4 letters are just chosen.\r
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\n" ); document.write( "\n" ); document.write( "      To assert this is to pervert the problem.\r
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\n" ); document.write( "\n" ); document.write( "      He solves the problem in his interpretation; me - in my interpretation.\r
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\n" ); document.write( "\n" ); document.write( "The fact that two different interpretations are possible means
\n" ); document.write( "a crash, a catastrophe and a death sentence for this problem,
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\n" ); document.write( "\n" ); document.write( "Obviously, the person who created this problem, is unprofessional Math composer
\n" ); document.write( "and creates his compositions \" kneeling in the garage \", even without reading any Math textbooks
\n" ); document.write( "and learning Math exclusively from reading this and other Internet web-sites.\r
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\n" ); document.write( "\n" ); document.write( "A correctly worded and the ONLY POSSIBLE question should be \" how many different passwords are possible ? \" \r
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