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