N is a 9-digit perfect square, with no leading zero, which is constituted by each of the nonzero base ten digits from 1 to 9 occurring exactly once.

Determine the probability that the positive square root of N is a positive integer having the form AB0CD, where each of A, B, C and D represents a different base ten digit from 1 to 9.

As a bonus, what is the probability, if the base ten digits represented by A, B, C, D are not necessarily different?

Note: The "0" inclusive of the string "AB0CD" is the digit zero, and not the letter O.