document.write( "Question 887963: How many nine-digit numbers can be formed using all the digits from 1 to 9, if the odd digits must always be in ascending order and the even digits in descending order? \n" ); document.write( "
Algebra.Com's Answer #536999 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Among the 9 digits 1,2,3,4,5,6,7,8,9, \r\n" );
document.write( "the 5 odd digits must appear \r\n" );
document.write( "in the order 1,3,5,7,9, left to right \r\n" );
document.write( "and the 4 even digits must appear \r\n" );
document.write( "in the order 8,6,4,2,left to right \r\n" );
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document.write( "Of the 9 positions in the 9-digit number, we can choose\r\n" );
document.write( "the 4 positions for the even digits in C(9,4) = 126 ways.\r\n" );
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document.write( "[Notice that although the even digits must be in a certain order,\r\n" );
document.write( "order does not matter when we are picking the positions in which\r\n" );
document.write( "the even digits will appear in the 9-digit number.  For example, in\r\n" );
document.write( "the 9-digit number 123546789 we are picking positions 2,5,6, and 8 \r\n" );
document.write( "for the even digits to go in.  Notice that picking positions 5,8,2, \r\n" );
document.write( "and 6 is the same set of positions as the set of positions 2,5,6, \r\n" );
document.write( "and 8 or positions 8,5,6, and 2. Therefore order of POSITIONS picked \r\n" );
document.write( "DOES NOT matter!  That's why we use combinations rather than \r\n" );
document.write( "permutations.  Hope this doesn't confuse you!]\r\n" );
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document.write( "The odd digits will be placed in ascendng order in the remaining 5 \r\n" );
document.write( "positions in just C(5,5)=1 way.\r\n" );
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document.write( "Answer C(9,4) = 126 ways\r\n" );
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document.write( "Edwin
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