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How many distinct even numbers less than 1000 can be formed by using only the
\n" ); document.write( "numbers {0, 2, 5, 6, 9}; when repetition of a number is not allowed?
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document.write( "One digit numbers:\r\n" );
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document.write( "The even one-digit numbers are 0, 2, and 6. That's 3 one-digit numbers. \r\n" );
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document.write( "Two-digit numbers:\r\n" );
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document.write( "A. If we choose 0 for the second digit, then there are 4 choices for the first\r\n" );
document.write( "digit. That's 4 two-digit even numbers, 20, 50, 60, and 90. \r\n" );
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document.write( "B. If we do not choose 0 for the second digit, then there are 2 choices for the\r\n" );
document.write( "2nd digit (2 or 6). That leaves 3 choices for the 1st digit. That's 2×3 or 6\r\n" );
document.write( "more even two-digit numbers, 52,92,56,96,26,56\r\n" );
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document.write( "Total number of two-digit numbers = 4+6 = 10\r\n" );
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document.write( "Three-digit numbers:\r\n" );
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document.write( "We can make each of the 10 two-digit numbers into a three digit number in 3\r\n" );
document.write( "ways, by inserting any one of the remaining 3 digits between them. So the\r\n" );
document.write( "total number of three-digit even numbers is 10×3 = 30\r\n" );
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document.write( "Total: 3+10+30 = 43 even numbers, with no repeated digits, using only the\r\n" );
document.write( "digits {0, 2, 5, 6, 9}.\r\n" );
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document.write( "Here are all 43:\r\n" );
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document.write( "0, 2, 6,\r\n" );
document.write( "20, 26, 50, 52, 56, 60, 62, 90, 92, 96,\r\n" );
document.write( "206, 250, 256, 260, 290, 296, 502, 506, 520, 526\r\n" );
document.write( "560, 562, 590, 592, 596, 602, 620, 650, 652, 690\r\n" );
document.write( "692, 902, 906, 920, 926, 950, 952, 956, 960, 962\r\n" );
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document.write( "Edwin \n" );
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