Winning the Lottery
Professor Slavy buys a lottery ticket, which requires that he pick six different integers from 1 through 46, inclusive.
He chooses his numbers such that the sum of the base-ten logarithms of his six numbers is an integer.
It so happens that the integers on the winning lottery ticket have the same property- the sum of the base-ten logarithms is an integer.
What is the probability that Prof. Slavy holds the winning ticket?