document.write( "Question 1111294: Five digit numbers are made using the numbers 0 to 7. Determine the number of odd numbers that can be made if each digit can only be used once. \r
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Algebra.Com's Answer #726276 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "If it is allowed in this problem for five digit numbers to start from the zero digit, then the solution by other tutor is good.\r
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\n" ); document.write( "\n" ); document.write( "But it is commonly assumed in the everyday life that, when consider \"n-digit numbers\", then the first digit is not \"0\".\r
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\n" ); document.write( "\n" ); document.write( "Under this constraint, the solution of the previous post must be changed in this way:\r
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document.write( "1.  Choose the \"units\" digit by any way among 1, 3, 5 or 7.\r\n" );
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document.write( "    You will have an odd number, and you have 4 options at this step.\r\n" );
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document.write( "2.   As the left-most, you can choose any of remaining 8-1 = 7 digits EXCEPT zero. \r\n" );
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document.write( "     So you have (8-1)-1 = 6 options in all at this step.\r\n" );
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document.write( "3.  For  2-nd position from the left, you have 8-2 = 6 options among remaining digits.\r\n" );
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document.write( "    For  3-rd position from the left, you have       5 options among remaining digits.\r\n" );
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document.write( "    For  4-th position from the left, you have       4 options among remaining digits.\r\n" );
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document.write( "4.  In all, you have  4*6*6*5*4 = 2880 choices and 2880 of 5-digit different odd numbers.\r\n" );
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