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
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.