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February 13th, 2010, 12:02 AM  #1 
Member Joined: Nov 2006 Posts: 54 Thanks: 0  12digit number occurrence determination
For a 12digit base ten positive integer N constituted entirely by odd digits, determine the probability that N contains each of the digits 1, 3, 5, 7, 9 at least twice, but at most three times.

February 13th, 2010, 07:48 AM  #2 
Senior Member Joined: Feb 2009 From: Adelaide, Australia Posts: 1,519 Thanks: 3  Re: 12digit number occurrence determination
Any such number can be rearranged as a string of the form 1133557799xy where x<y. The number of ways to choose x and y is ; then for each choice of x and y the number of distinguishable permutations is . The product is 16632000, and dividing by 5¹² we find the probability is 6.8125 %.


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12digit, determination, number, occurrence 
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