Can you get an infinite amount of possibilities with a finite amount of things?

Yes. Love is beyond math.

 yes - so long as the sum of all those possibilities is no greater than 1 (certainty)

There is a potentially uncountably infinite amount of things

to know about any physical object including, of course,

the Cheerio in question.

Knowledge, however, is at most countably infinite,

and the amount we can know in any finite time is definitely finite.

Thus, as far as learning for any individual is concerned,

the task is certainly finite.

A guitar has 6 strings but an infinite number of tunes can be played on it.

A discussion about the Axiom of Choice would take lots of space.

To bring it down a notch, try this:

There are (in base 10) a finite number of digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9).

Their placement in a number determines the value of each digit within the number.

For example, the number 1234 has a value of:

1 x 1000, plus

2 x 100, plus

3 x 10, plus

4 x 1.

What is the largest number that can be represented using this simple, finite set of rules and objects?

There is no finite number that can serve as this "largest number". The list of possible numbers is, therefore "infinite" (which literally means "not finite").

Yes, I believe the universe to be infinite, not the local expanding known universe but the broader void into which it expands. Therefore an object, any object can be placed in an infinite number of places.

What about the infinite monkey cage, an infinite amount of monkeys bashing at an infinite number of keyboards would eventually write the complete works of Shakespeare.. therefore the finite works of Shakespeare create an infinite amount of incorrect versions when set as a task for an infinite amount of monkeys.

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If by 'possibilities' you mean selections, combinations and permutations, then no.  If you roll a pair of dice a finite number of times, or pick three cards from a deck a finite number of times, you get a finite number of possibilities.  Large, but finite.

In order to get an infinite number of possibilities, you need dice with an infinite number of sides, or decks of cards with an infinite number of cards.  And I know such things don't exist, because if they did, they'd be used in casinos!

There are a finite amount of digits, 0, 1, 2, 3,...., 9

There are an infinite number of numbers that can be represented with finite strings of those digits.

"1"

"2"

...

"10"

Not that each string has a finite number of digits in each string, but that the number of strings that can be represented is infinite.

I can give you infinite with just 1 'thing'.

Digits in pi, the ratio of the circumference of a circle to it's diameter.

What u mean I don't have an appointment