One important thing to remember is that Sir Arthur is a Brit, so his billion is a million million, a US trillion, 10 to the 12, which is the number of 12 letter words in a 10 letter alphabet, so his estimate is not that far off. Also, if I remember correctly, there were restrictions (i before e except after c ???
, not every string was a name of God. It would take a computer a while to make the calculation at the time the story was written. With today's terraflop computers, I don't think it would take very long at all.
There is a problem in printing it out. Assume a thousand words a page, with pages bound into books, with a thousand pages per book, we need a million books, all different. Not impossible, but difficult, especially since paper needs to be carried by porters up a twisty mountain road.