Professor Gamble buys a lottery ticket, which requires that he pick six different integers from 1 through 46, inclusive. He chooses his numbers so that the sum of the base-ten logarithms of his six numbers is an integer. It so happens that the integers on the winning ticket have the same property- the sum of the base-ten logarithms is an integer. What is the probability that Professor Gamble holds the winner ticket?
Answer Choices
A. 1 / 5
B. 1 / 4
C. 1 / 3
D. 1 / 2
E. 1