document.write( "Question 838890: How many distinct 4 digit numbers can be formed from 1, 1, 2, 2, 2, 3, 4? I have found many problems with one digit repeating that remove the repeated numbers by division, but I can't figure out what to do with 2 repeating digits aside from lists which are rather inefficient. (7*6*5*4)/(3! +2) is the closest to what I believe to be the answer. \n" ); document.write( "

Algebra.Com's Answer #507324 by Edwin McCravy(20055) $\"\"$ $\"About$

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1, 1, 2, 2, 2, 3, 4
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document.write( "There are 4 types of 4-digit numbers to get all the permutations of.  These 4\r\n" );
document.write( "types are ABCD, AABC, AABB, and AAAB.\r\n" );
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document.write( "1.  ABCD There is only one of this form, 1234.  That accounts for 1 form times\r\n" );
document.write( "4! or 24 ways to arrange it.\r\n" );
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document.write( "2.  AABC We can choose the digit for A 2 ways, For each of those ways, we can\r\n" );
document.write( "choose the B and C any of C(3,2)=3 ways. That accounts for  2×3 = 6 ways to\r\n" );
document.write( "choose the digits to rearrange, (They are 1123,1124,1134,2213,2214,2234).  Each\r\n" );
document.write( "of these 6 can be rearranged in  = 12 ways.  That's 6×12=72 ways.   \r\n" );
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document.write( "3.  AABB.  This is the number of ways to rearrange 1122 which is  = 6 ways.    \r\n" );
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document.write( "4.  AAAB. The digit for A must be 2.  There are then 3 choices of digits for B.\r\n" );
document.write( "(These are 2221,2223,2224). Each of those can be arranged  = 4 of each\r\n" );
document.write( "of this form).  That's 12 ways.\r\n" );
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document.write( "Total: 24+72+6+12 = 114 ways.\r\n" );
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document.write( "Edwin

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