Hello, Vicky!

Professsor Gamble buys a lottery ticket, which requires that he pick six different integers from 1 -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?

Suppose the winning numbers are: .

The sum of the six logs is an integer: .

This means that the log of theof the numbers is an integer: .product

. . Hence: .

That is, the product of the 6differentnumbers is a power of 10.

I found onlycases:four

. .

Therefore, the Professor's probability of winning is