Mathematicians who believe the universe is infinite state that anything that is possible will occur an infinite number of times. So, an infinite number of monkeys, with an infinite number of typewriters, will type the complete works of Shakespeare an infinite number of times. Certainly, in an infinite universe that is a possibility.
But, in an infinite universe where anything possible will happen those same monkeys will not type the complete works of Shakespeare but will just type the letter "a" an infinite number of times because that too is possible.
But even within an infinite universe those two outcomes cannot exist at the same time because that would be an impossibility.
So, an infinite universe where everything that can possibly happen will occur cannot exist because certain possibilities cannot exist in the same space. Therefore the universe is finite.
Alternatively, of course, the universe could be infinite but not everything that can possibly happens occur. For example, mathematicians will state that in an infinite universe the earth will be duplicated an infinite number of times, because eventually a finite number of particles have to form themselves into repeating patterns as there is a limit to the number of different patterns they can form (see billiard balls). But, even in an infinite universe it could be the case that complex forms stop at a certain point and the rest of infinity is full of dust particles, bananas or nothing.