I agree that a million or a “hundred QUINTILLION” years probably wouldn’t produce the play. It seems to me, though, that once you assume that the letters will be randomly combined and assume an infinite amount of time, you have to conclude that eventually Shakespeare’s play will be produced. It doesn’t matter how hard it is to find strings of 20 or so common words on the internet.
I post on language forums, and often a good test for whether a three or four word combination is idiomatic in a language is simply to do a net search for it (and if there are only a few results, make sure the results aren’t from non-native speakers). You rightly point out, though, that if the words in the phrase are unusual or the string of words longer than just a few, it’s unlikely to be found and can’t be checked that way.
According to Google, your sentence just appears here, and “The girl grabbed onto the back” just occurs at one other site. Google numbers for search results vary for several reasons and aren’t reliable, but there are 7,560 for “The girl grabbed onto”, and 319,000 for “The girl grabbed”. That’s with the internet being a relatively recent phenomenon in historical terms. Imagine a million internet monkeys typing away for millions of years — no, for an infinity of years. Then, I suspect, they’d have something.
Please keep in mind that this whole monkeys typing Shakespeare was used as an example to justify evolution. Lightening striking a tide pool (hot dilute chemicals) you would eventually get life started. Then entered the monkeys with typewriters. So if you could get Shakespeare you can get life started.
my memory fades with time but if you took the number of DNA strands and the number of DNA combination the number of also quite large.
I believe we have disproved the monkeys with typewriters as an impossibility. And like the random lightening strikes is also an impossibility.