When making a decision, how many “choices” are there?

Question

Suppose I put a coin on a table. I can do this in two ways: heads up or heads down.

Question: How many choices do I make?

It looks like I have one choice in the sense of having one decision. But, at the same time, I have two options (which is a synonym for "choice"; ref. Wiktionary, Thesaurus.com), so we could also say that I have two choices too.

This grammatical situation arises frequently in combinatorial mathematics; some random examples are

When you have n things to choose from ... you have n choices each time! -- MathsIsFun.com

and

You can count the number of permutations of a set of n elements in the following way: there are n choices for the first item, then (n-1) choices for the second item, and after choosing those two, (n-2) choices for the third item, and so on. -- Albyn Jones

In both of these cases, there is a single decision to be made at each step, but there are (in general) multiple options.

Answer 1

What's the problem? Choice has two related but different meanings; or in fact, three: the act or event of choosing, the possible options, and the one actually chosen.

I suppose you could possibly come up with a context in which there might be ambiguity between these, but it is unlikely, and we know this because there are these three meanings. If real ambiguity had arisen often, it is likely that the language would have adjusted itself to avoid the ambiguity.

The are plenty of similar examples: a cut is what you do with a knife, but also the result of that action (in a piece of paper, or your finger). Sight is what you do with your eyes, but also in some contexts the thing you see.