Understanding the Graph of a Multinomial Distribution

Question

I am trying to understand exactly what information the graph of a multinomial distribution is supposed to convey.

The thing I find strange is that a binomial distribution is graphed in two dimensions and contains information about two fundamental outcomes, i.e., heads and tails on a coin. I would expect the three dimensional graph of a multinomial distribution to describe a "three-sided coin."

However, in Mathematica, the function for a multinomial distribution only allows two outcomes to be entered, and they must sum to probability $1$, leaving no room for an implicit third outcome.

The multinomial distribution graph in three dimensions seems to contain exactly the same information as the binomial distribution graph in two dimensions. In fact, the nonzero data can be seen (in the above example and in the Mathematica documentation) to be contained within a two-dimensional, diagonal slice of three-dimensional space.

Should a three-dimensional multinomial distribution PMF describe three fundamental outcomes, or if not, what extra information does the extra dimension allow?

Answer 1

Removed original post for not answering the question

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Edit

From the documentation:

It appears that you are really only plotting a binomial distribution, you just happen to be plotting it with 2 axes, but it is intrinsically binomial as you can see above - all nonzero probabilities lie on the line $x + y = 10$.

Further, you can see that when you only input two probabilities (the In[2] line) that you get a PMF which corresponds to a binomial (Out[2]). When you input 3 probabilities, you get a truly multinomial distribution, as evidenced by In[3] and Out[3].

I guess this is just the syntax/definition that Mathematica uses - I don't use it much.