To go back to the Borges post earlier, and the idea that "in an infinite period of time all things happen to all men." An example of this notion being the infinite monkeys on typewriters producing the works of Shakespeare given infinite time.
This understanding views time and circumstances as akin to a roulette wheel of time spinning, and with the numbers on the wheel representing what is imagined to be the full possible gamut of circumstances, and that within an infinity of time the ball must eventually fall into each possible slot. However, if all the circumstances can be represented on the roulette wheel, then they must be a finite set of circumstances, not infinite. Infinity cannot be meaningfully spoken of in the inclusive sense of "all that is within infinity." The inclusiveness of 'all' necessarily a notion reserved for use of finite terms.
This lucidly demonstrated by the mathematical parallel of "all the numbers within infinity." Take one of these numbers within the infinity of numbers; this being Pi. Pi- the ratio of any circle's circumference to its diameter- is itself infinite, and so one cannot speak of 'all the numbers of Pi'; 'all' being an inclusive term, whereas infinity spills endlessly beyond 'all'. And this Pi is but one number within an infinity of numbers. Interestingly, Pi is what is described as a transcendental number . It transcends finite representation: though this may have a somewhat different specific meaning in the language of mathematics its linguistic sense holds true.
And any single circumstance of life can be paralleled with Pi. No element within life can be abstracted from the whole of life without falsifying both- there being no life and its consituents distinct from each other, and so each circumstance is itself necessarily an infinity. We cannot cut life into segments or impose limits whereby something is a self-enclosed individual event or circumstance. So, for example, the circumstance of a man standing up exists simultaneously on all kinds of fronts, but to take one element of its existence being the visual. The action could be witnessed from an infinity of points, and such points of perspective could not be exhausted, else they would be a finite number, not infinite. So on that front alone, it is an infinite event, not finite. Though this infinity of points of perspective are infinite, not because of linguistic tautological reasons, but because this is the nature of reality. Every square inch of space is infinite.
So all in all, to talk of 'the infinity of possible things that must happen within infinity' is senseless even on pure linguistic terms. When we try to reach infinity from an assumed starting point of the reality of the finite, we can but end in nonsensical absurdism, but this deluded belief in the solid reality of the finite tends to be the starting point for all discursive thought.
By the way, the mathematical probablitities of the notion of the random creation of Shakespeare's works by undirected intelligences in the form of monkeys is examined here, where the humbler likelihood of the monkeys producing but a single line of Shakespeare is put to the test.