"? People who don't have a clue about combinatorics tout "billions of years," not realizing that it is about 1000 orders of magnitude too little."
People who have NO clue about probability spout wildly improbable figures about the probabilities of processes they know nothing about.
When man is able to produce life in the lab, {shouldn't be a problem since it happened by accident} I figure the probability is high we'll hear all about it.
A famous evolutionist once famously said that a monkey typing randomly would eventually pound out Macbeth. As famous and educated as he was, he was truly clueless about combinatorics. Yet the notion he espoused -- that anything can happen given enough random events -- is one of the key ideas behind evolution.
Someone with a bit more understanding of combinatorics did an actual calculation. I don't remember the details off hand, but it went something like the following. If you filled the entire known universe with one monkey per cubic yard and had them type randomly at a very high rate for the entire known age of the universe, chances are vanishingly small that they would ever get past the first page of Macbeth.
By the way, I scored a 4.0 in Probability and Statistics as an undergrad -- not bad for someone with "NO clue about probability"! I believe I was in the top one or two of a class of around 60. That was a while ago, however.