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February 13th, 2010, 12:02 AM   #1
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12-digit number occurrence determination

For a 12-digit 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.
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February 13th, 2010, 07:48 AM   #2
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Re: 12-digit 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 5 we find the probability is 6.8125 %.
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