document.write( "Question 970210: Hi, \r
\n" ); document.write( "\n" ); document.write( "Please can you tell me how many different combinations there are to the following question:\r
\n" ); document.write( "\n" ); document.write( "Write all the four-digit even numbers greater than 5000 that can be made using these digits. You may only use each digit once in a number.\r
\n" ); document.write( "\n" ); document.write( "2 4 6 5 8\r
\n" ); document.write( "\n" ); document.write( "My friend found 12 combinations, my daughter 24 and so far I'm up to 27!!\r
\n" ); document.write( "\n" ); document.write( "Please help...\r
\n" ); document.write( "\n" ); document.write( "Thanks\r
\n" ); document.write( "\n" ); document.write( "Kirsty \n" ); document.write( "
Algebra.Com's Answer #592914 by AnlytcPhil(1806)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "It turns out that there are 60.  Heres why: \r\n" );
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document.write( "Case 1:\r\n" );
document.write( "If we choose 2 or 4 for the last digit, there will be 3 ways remaining\r\n" );
document.write( "to choose the first digit.  They will be 5,6 or 8  \r\n" );
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document.write( "There are 2 ways to choose the last digit so that there will be 3\r\n" );
document.write( "ways to choose the first digit. So for each of those 2 ways to choose\r\n" );
document.write( "the last digit, there are 3 remaining ways to choose the first digit. \r\n" );
document.write( "So that's 2x3=6 ways. \r\n" );
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document.write( "Case 2:\r\n" );
document.write( "If we choose 6 or 8 for the last digit, there will be only 2 ways remaining\r\n" );
document.write( "to choose the first digit.  There will be 5 and the remaining one of 6, 8.  \r\n" );
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document.write( "There are 2 ways to choose the last digit (as 6 or 8) so that there will be \r\n" );
document.write( "only 2 ways to choose the first digit. So for each of those 2 ways to choose\r\n" );
document.write( "the last digit, there are 2 remaining ways to choose the first digit. \r\n" );
document.write( "So that's 2x2=4 ways.\r\n" );
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document.write( "That's a total of 6+4 or 10 ways to choose the first and last digits.  \r\n" );
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document.write( "For each of those 10 ways to choose the digits on the two ends, we can\r\n" );
document.write( "choose any of the the remaining 3 digits for the second digit.  That's\r\n" );
document.write( "10x3 or 30 ways to choose the last, first, and second digits.\r\n" );
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document.write( "For each of those 30 ways to choose the first second and last digits, \r\n" );
document.write( "we can choose either of the the remaining 2 digits for the third digit.\r\n" );
document.write( "That's 30x2 or 60 ways to choose all four digits so that the number\r\n" );
document.write( "will be even and greater than 5000.\r\n" );
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document.write( "Here is a computer printout of all 60 even numbers\r\n" );
document.write( "greater than 5000 that can be made with 2,4,6,5,8.\r\n" );
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document.write( "5246 5248 5264 5268 5284 5286 5426 5428 5462 5468 \r\n" );
document.write( "5482 5486 5624 5628 5642 5648 5682 5684 5824 5826 \r\n" );
document.write( "5842 5846 5862 5864 6248 6254 6258 6284 6428 6452 \r\n" );
document.write( "6458 6482 6524 6528 6542 6548 6582 6584 6824 6842 \r\n" );
document.write( "6852 6854 8246 8254 8256 8264 8426 8452 8456 8462 \r\n" );
document.write( "8524 8526 8542 8546 8562 8564 8624 8642 8652 8654 \r\n" );
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document.write( "Edwin
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