document.write( "Question 843372: how many even numbers between 300 and 800 can be formed using the elements from the set {1,2,4,5,6,9} if no elements can be used more than once? \n" ); document.write( "
Algebra.Com's Answer #508457 by Edwin McCravy(20055)\"\" \"About 
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document.write( "We must choose the first digit as 4,5 or 6, but since the\r\n" );
document.write( "last digit must be 2,4, or 6 it will be a different number\r\n" );
document.write( "of even numbers if we choose 5 for the first digit than if\r\n" );
document.write( "we choose 4 or 6 for it.  So we consider three cases.\r\n" );
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document.write( "Case 1.  We choose 4 for the first digit.\r\n" );
document.write( "         We choose the last digit any of 2 ways. (2 or 6)\r\n" );
document.write( "         We choose the middle digit any of the remaining 4 ways.\r\n" );
document.write( "         That's 1󫏀 = 8 ways. \r\n" );
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document.write( "Case 2.  We choose 5 for the first digit. \r\n" );
document.write( "         We choose the last digit any of 3 ways, {2,4, or 6}\r\n" );
document.write( "         We choose the middle digit any of the remaining 4 ways.       \r\n" );
document.write( "         That's 1󫢬 = 12 ways.\r\n" );
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document.write( "Case 3.  We choose 6 for the first digit.  That's the same as case 1,\r\n" );
document.write( "         So that's also 8 ways.\r\n" );
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document.write( "Answer: 8+12+8 = 28 ways.\r\n" );
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document.write( "Here are all 28 ways,\r\n" );
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document.write( "412 416 426 452 456 462 492\r\n" );
document.write( "496 512 514 516 524 526 542\r\n" );
document.write( "546 562 564 592 594 596 612\r\n" );
document.write( "614 624 642 652 654 692 694\r\n" );
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document.write( "Edwin
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