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

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.

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I deleted the "grammar" tag: this isn't a grammar Q but a word-choice & word-usage Q. Semantics and style are the issue, not grammar. While choice and option are sometimes synonyms, they aren't interchangeable: usage rules are different. You make a choice and {choose/select} an option; you {choose/opt for} heads. Because most speakers don't see much of a semantic difference between these two words in common parlance, which one you use is strictly a style {choice/option}, unless your field stipulates exclusive definitions. M-W.com doesn't list choice as a synonym for option. – user21497 Sep 23 '12 at 12:02
You will ask "what are my choices?" You will be asked "What is your choice?" -- the two occurrences of the word do not have the same implication. The word is the same, the concept is also the same. However, the context differs and the sense differs accordingly. – Kris Sep 23 '12 at 13:57