I've got 4 balls and 4 boxes - explain how I work out the number of arrangements

I have 4 balls, numbered 1-4 or different colours - basically 4 balls all different.

I have a box - I'll call it my universe.

In this box I can arrange the balls

12

34

23

14

and so on. NO REPEATS are allowed.

How do I calculate - with an explanation - how many different arrangements I have.

I think the answer should be 16.

Can anyone explain?

Not according to Max Tegmark

THe reason why I asked this is that I saw this article by Max Tegmark. According to him 16 is the answer. I cannot imagine a physicist getting it wrong. I've copied below what he wrote. He also draws a diagram...not shown here. What am I missing from this description - in understanding - that gives him 16 arrangements? I don't get it.

EXAMPLE UNIVERSE

Imagine a two-dimensional universe with space for four particles.

Such a universe has 2^4, or 16, possible arrangements of matter.

If more than 16 of these universes exist, they must begin to

repeat. In this example, the distance to the nearest duplicate is

roughly four times the diameter of each universe.

Looking at the diagram it shows this

It looks as if what he's describing is being able to put 4 particles in any combination within 4 boxes

so for example: white and grey particles - are shown in the diagram. So perhaps he's saying 4 particles but two one kind and two of another?

white, white

grey, white

grey, white

grey, grey

and so on.

So perhaps I misread it. He didn't say that though!

Are you able to explain how this is worked out then please?

Hi Okay, are you able to tell me how one gets to the 2 to the power of 16 with this particular situation please?

THe formula used, why and how please?