A five digit positive integer is a mountain number if the first three digits are in strictly ascending order and the last three digits are in strictly descending order. For example, 46872 is a mountain number, but none of 43434, 54456 and 46766 is a mountain number.

Determine the probability that N is a mountain number, given that N is a positive integer chosen at random between 40000 and 99999 inclusively.

The problem, as stated, does require that we have "a five digit positive integer" and that 1st 2nd 3rd are "strictly ascending" and 3rd 4th 5th are "strictly descending" -- and also that the range for N is 40000 - 99999, though we would only need to consider those between 45610 and 78987.

I haven't encountered the concept of "mountain number" elsewhere, so I guess KS may define it as he pleases. Clearly to extend this puzzle, other definitions may be explored, as several have done, though each would have to define a new test. Perhaps "not less/more than" instead of the strictly increase/decrease; or, what is the frequency of palindromes. Or, we could have "valley numbers" with the reversed criteria, etc. The range of numbers would need to be specified, so that "probability" had its denominator.