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I'm trying to calculate the probability that a five digit mountain number (i.e. a number in which the first three digits are in ascending order i.e. $a< b< c$, and the last three are in descending order i.e. $c> d> e$) does not contain any repeated digits. I've calculated that there are $2892$ mountain numbers, simply by looking at how many possibilities there are on each side with each peak (i.e. $36^2+28^2+...+1^2$). I wrote a small program that output the number of mountain numbers without repeating digits($1512$), but I'm not sure how I would get to that number with out the help of a computer. Could anybody help me out here? Thanks!

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