What a math fail. Shuffling a deck of cards or labeled blocks should be used for this example, not dice (I think sjestus was trying to say 'label each die with only one letter'). In the end it doesn't really matter but it had me scratching my head as I was trying to figure out what the probability space was for a moment.
Lol, he (or she) can't even write the product for the factorial correctly. We write 20!=20x19x18x...x1 to get the point across. Writing 1x2x3x4x... would be an infinite product that formally diverges, but can be assigned the value sqrt(2pi) by zeta regularization.
And as already stated 20! isn't 10347, it's not even close to the same order of magnitude. And it's really easy to see they are not the same; 10=5x2, so any power of 10 is only divisible by numbers that factor into powers of 2 and 5. But 20! clearly has factors that aren't 2 and 5, so 20!=/=10347. And in general there are no numbers m and n in the positive integers such that n!=10m.
An easy way to see how much the order of magnitude is off is that clearly 20!<2020 and clearly 2020<1040. So 20! must be far less than 10347.
I do think that sjestus was trying to say 20! is on the same order of magnitude as 10347 and not trying to say they are exactly equal, but in either case it's so horrendously wrong that no leniency can be given.
The original thread on RR is gone now, but I'm assuming it was the stupid 'life could never just happen because probability' argument. Unfortunately for creationists the universe rolls lots of sets of dice, and it had been rolling dice for roughly 9.4 billion years when the Earth started forming, and it only had to continue rolling for another 0.5-0.7 billion years until life got started on Earth. So life is probably not that hard to make.
Besides math, another issue with this is that the argument assumes we just throw away correct subsequences of what has been rolled if the whole sequence wasn't the result we were looking for. Biology (and in this case the synthesis of self replicating organic molecules) doesn't work that way, what works is selected for and gets to stay around for the next trial.
Also what Darth Wang said, that's one of the biggest things that dismantles this argument.
tl;dr fundies can't do math
@Bandersnatch
Nah, the probability they were going for was 1/(20!). Which is the odds of taking all the labeled blocks out of the box (or whatever) one at a time with no replacement and having them come out in the order A, B, C, ..., S, T in one trial. (And as Bob and Frumious B. point out, it's also the odds of getting any other result in just one trial.)
@547772
That's not really true, if some event had a 1/n chance of occurring we would expect to see it once in n trials, but it doesn't have to come up in that number of trials.
For example, it's possible to roll a 6 sided die 6 times and never see a 3 come up.