document.write( "Question 1106687: How many two-digit even numbers can you form using the digits 0, 1 , 2, 3, 4, 5, 6, 7, 8, 9?
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Algebra.Com's Answer #721680 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "How many two-digit even numbers can you form using the digits 0, 1 , 2, 3, 4, 5, 6, 7, 8, 9?
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document.write( "Of the 10 digits, 5 are even.  So in both cases there are 5 choices for the units digit of the 2-digit number.\r\n" );
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document.write( "(a) If repetition is allowed, then there are 10-1 = 9 choices for the tens digit.  \r\n" );
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document.write( "    (9 because you can not use zero as the \"tens\" digit).\r\n" );
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document.write( "    The total number of possible 2-digit even numbers is 9*5 = 45,  if repetition is allowed.\r\n" );
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document.write( "(b) If repetition is not allowed, then there are two cases.\r\n" );
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document.write( "    Case 1.  The \"units\" digit is zero. Then you have 9 choices for the \"tens\" digits.\r\n" );
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document.write( "             Hence, 9 (nine)  2-digit numbers are possible, ending by \"0\".\r\n" );
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document.write( "    Case 2.  The \"units\" digit is any of 4 even digits 2, 4, 6 or 8. \r\n" );
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document.write( "             Then you have 8 choices for the \"tens\" digit.\r\n" );
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document.write( "                  (Only 8, because you can not use zero and just used \"units\" digit).\r\n" );
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document.write( "             Hence, 8*4 = 32  2-digit numbers are possible in this case.\r\n" );
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document.write( "             The total  for  case 1 + case 2  is  9 + 32 = 41.\r\n" );
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document.write( "             So, in this problem / (sub-problem) the answer is:  41  2-digit even numbers are possible,  if repetition is not allowed.\r\n" );
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\n" ); document.write( "Notice that the answers to (a) and (b) are CONSISTENT:\r
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document.write( "    From 45 numbers of the set (a) you need exclude four numbers 22, 44, 66  and 88  to get  41 number of the set (b).\r\n" );
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