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.

Using Excel, there are 606 mountain numbers within that range of 60000 integers.  Thus the probability is 1.01%.

Another way to solve would be to figure out probabilities for all three-digit ascending numbers and the three-digit descending numbers sharing the same digit.

Posted by hoodat on 2010-04-20 00:37:30