document.write( "Question 1133681: how many positive odd numbers can be formed from the digits 2,3,4,5,6 if no digit is to be repeated in a given number
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Algebra.Com's Answer #750932 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "I took it that you meant to use ALL 5 digits.  The other tutor took it that\r\n" );
document.write( "you want 1-digit numbers, 2-digit numbers, etc., all the way to 5-digit\r\n" );
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document.write( "Any odd number ends with an odd digit.\r\n" );
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document.write( "We choose the most restrictive digit first, which is the last digit.  The\r\n" );
document.write( "last digit can only be one of these two digits 3 and 5. So.\r\n" );
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document.write( "We can choose the last digit any of 2 ways.  That will leave 4 unchosen\r\n" );
document.write( "digits.\r\n" );
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document.write( "For each of the 2 ways we can then choose the last digit, we can choose the\r\n" );
document.write( "first digit as any of the 4 remaining unchosen digits.\r\n" );
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document.write( "So we can choose the last and first digits any of 2x4 ways. (8 ways)\r\n" );
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document.write( "That leaves 3 unchosen digits.\r\n" );
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document.write( "For each of the 2X4 or 8 ways we can choose the last and first digits, we\r\n" );
document.write( "can choose the second digit as any of the 3 remaining unchosen digits.\r\n" );
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document.write( "So we can choose the last, first and second digits as any of 2x4x3 ways.\r\n" );
document.write( "(24 ways)\r\n" );
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document.write( "That leaves 2 unchosen digits.\r\n" );
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document.write( "For each of the 2X4x3 or 24 ways we can choose the last, first and second \r\n" );
document.write( "digits, we can choose the third digit as either of the 2 remaining unchosen\r\n" );
document.write( "digits.\r\n" );
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document.write( "So we can choose the last, first, second and third digits as any of 2x4x3x2\r\n" );
document.write( "ways.  (48 ways)\r\n" );
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document.write( "That leaves only 1 unchosen digit. We must choose that final fourth digit as\r\n" );
document.write( "that 1 remaining unchosen digit.  We can choose it only 1 way. So the final\r\n" );
document.write( "answer is 2x4x3x2x1 = 48 ways\r\n" );
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document.write( "Edwin
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