document.write( "Question 1208272: What is the number of different five-digit numbers that can be formed from the set S={2,3,4,5,6} such that one digit is repeated twice and another digit is repeated twice \n" ); document.write( "

Algebra.Com's Answer #846584 by Edwin McCravy(20055) $\"\"$ $\"About$

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document.write( "When a digit is repeated three times, it is repeated two times. \r\n" );
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document.write( "They are either the arrangements of XXYYZ or of XXYYY, where different\r\n" );
document.write( "letters represent different digits.\r\n" );
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document.write( "Case 1.  The arrangements of XXYYZ.\r\n" );
document.write( "Choose the X 5 ways.\r\n" );
document.write( "Choose the Y 4 ways.\r\n" );
document.write( "Choose the Z 3 ways.\r\n" );
document.write( "That's (5)(4)(3)=60 ways.\r\n" );
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document.write( "We divide by two because, for instance, XXYYZ could be chosen respectively, as\r\n" );
document.write( "33556 or 55336, which are the same.\r\n" );
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document.write( "So that's 30 ways. to select the three digits.\r\n" );
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document.write( "They may be ordered in  distinguishable ways.\r\n" );
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document.write( "That's (30)(30) = 900 ways\r\n" );
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document.write( "Case 2: The arrangements of XXYYY\r\n" );
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document.write( "Choose the digit for X in 5 ways.\r\n" );
document.write( "Choose the digit for Y in 4 ways.\r\n" );
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document.write( "So that's (5)(4) = 20 ways.\r\n" );
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document.write( "Each may be permuted in  distinguishable ways.\r\n" );
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document.write( "That's (20)(10) = 200\r\n" );
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document.write( "For both cases, that's 900+200 = 1100.\r\n" );
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document.write( "Edwin

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