An

Ascending Number has been defined by the following 2 properties:

- The number has at least 2 digits.

- All digits of the number are in strictly ascending order, in base 10.

For completeness, let's also add: no leading zeros or duplicate digits.

For what value of N is the probability that a randomly chosen N-digit number is also an ascending number closest to .01, i.e. a 1% chance?

For this value of N, what is the exact probability the random number N digits long is ascending?