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how many 5 digit odd numbers can you make and no digit is repeated?
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document.write( "Always choose the most restrictive digit first. Then choose the next most\r\n" );
document.write( "restrictive, etc.\r\n" );
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document.write( "The most restrictive digit is the 5th because that's the one that \r\n" );
document.write( "determines that it is an odd number. So we will choose the fifth \r\n" );
document.write( "one first.\r\n" );
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document.write( "The next most restrictive digit is the first one, since it cannot\r\n" );
document.write( "be 0. So we will chose it second.\r\n" );
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document.write( "We can choose the 5th digit any of 5 ways, {1,3,5,7,9}\r\n" );
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document.write( "That's 5 ways to choose the 5th digit. Next we will choose the 1st\r\n" );
document.write( "digit.\r\n" );
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document.write( "Choosing the 5th digit leaves 9 digits not chosen. However one of \r\n" );
document.write( "those is 0, since we did not choose 0 for the 5th digit. And we \r\n" );
document.write( "cannot choose 0 for the first digit, so there are only 8 choices\r\n" );
document.write( "for the 1st digit. \r\n" );
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document.write( "So there are 5×8 or 40 ways to choose the 5th and 1st digits.\r\n" );
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document.write( "For each of those 5×8 or 40 ways to choose the 5th and 1st digits,\r\n" );
document.write( "there are 8 digits left to choose for the 2nd digit. (it CAN be 0).\r\n" );
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document.write( "So there are 5×8×8 or 320 ways to choose the 5th, 1st and 2nd digits.\r\n" );
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document.write( "For each of those 5×8×8 or 320 ways to choose the 5th, 1st, and 2nd\r\n" );
document.write( "digits, there are 7 digits left to choose for the 3rd digit.\r\n" );
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document.write( "So there are 5×8×8×7 or 2240 ways to choose the 5th, 1st, 2nd, and 3rd\r\n" );
document.write( "digits. \r\n" );
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document.write( "For each of those 5×8×8×7 or 2240 ways to choose the 5th, 1st, 2nd, and\r\n" );
document.write( "3rd digits, there are 6 digits left to choose for the 4th and final\r\n" );
document.write( "digit to choose.\r\n" );
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document.write( "So there are 5×8×8×7×6 or 13440 ways to choose the 5th, 1st, 2nd, 3rd,\r\n" );
document.write( "and 4th digits, with no digits repeated, which is the answer to the\r\n" );
document.write( "problem.\r\n" );
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document.write( "Edwin\r\n" ); document.write( "
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