"'infinite' doesn't necessarily mean 'contains all possibilities'. The sequence of all even numbers (246810121416182022...) is infinite, but the number '17' doesn't appear in it anywhere."
From the discussion following the posting of a color image generated from pi. That's about as succinct a refutation of the "monkeys typing Shakespeare" conundrum as I've ever come across.
Via a semi-random Ann Althouse link.
[But this follow-up, of the same pi derivation except in a radial arrangement, is a far cooler display.]