Gavin buys a lottery ticket, and in accordance with the rules he picks six different integers from through 1 to 46 inclusively. He chooses his numbers so that the sum of the base-ten logarithms of his six numbers is an integer.

By coincidence, the integers on the winning ticket have the same property - that is: the sum of the base-ten logarithms of the six numbers is an integer.

What is the probability that Gavin holds the winning ticket?