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.

There 606 "mountain number" integers between 40000 and 99999 inclusive.  The odds are 606 / 60000 or .0101 (exactly) .

Posted by ed bottemiller on 2010-04-07 11:40:37