document.write( "Question 1158403: How many numbers of 5 digits can be made from the digits 1,2,3,4,5,6,7,8 and 9 when each number contains exactly one even digit and no digit is repeated? \n" ); document.write( "

Algebra.Com's Answer #781352 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "ANSWER.  (4*5)*(5*4*3*2) = 20*120 = 2400.\r\n" );
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document.write( "Explanation\r\n" );
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document.write( "(1)  We can use any one of 4 even digits and can place it to any of 5 possible positions.\r\n" );
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document.write( "     It gives the factor 4*5 = 20.\r\n" );
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document.write( "(2)  Next we should place remaining 5 odd digits (1, 3, 5, 7 and 9) in remaining 4 positions. \r\n" );
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document.write( "        (Notice that after placing the even digit in #(1), its position and remaining positions are just \r\n" );
document.write( "        determined by a unique way - they are not a subject of choice anymore).\r\n" );
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document.write( "     Therefore, placing in #(2) can be done by 5*4*3*2 = 120 ways.\r\n" );
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document.write( "(3)  In total, it gives  20*120 = 2400 different ways, in accordance with the answer above.\r\n" );
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