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 winning ticket? <spanclass=′latex−bold′>(A)</span>1/5<spanclass=′latex−bold′>(B)</span>1/4<spanclass=′latex−bold′>(C)</span>1/3<spanclass=′latex−bold′>(D)</span>1/2<spanclass=′latex−bold′>(E)</span>1