Edit: Thanks for the clarification. I didn't realize that "synonym" had a technical meaning on Stack Exchange sites. Here's a quote from your link:
A tag synonym is usually a tag that has exactly the same meaning as some other tag, such as algorithm and algorithms. In some cases, tags that are subsets of other tags will also be considered synonyms, such as java-se for java.
The system organizes tags in a master/synonym relationship. All uses of the synonym tag(s) for any given master tag are automatically converted to the master tag. So, users can enter a synonym tag when writing a question, but the master tag will be displayed when the question is loaded. Similarly, when users search for questions tagged with a synonym, a list of questions tagged with the master will be displayed.
Although tag synonyms are allowed to be subsets of the master tag, I would hope that people wouldn't regard combinations as a large enough subset of combinatorics for it to be appropriate to identify them. From my perspective, tagging basic combinations problems combinatorics is like tagging basic derivative questions analysis. But when I look at how most combinations questions are tagged on this site, they generally get the combinatorics tag, not the combinations tag, so my view is clearly a minority one.
Original answer: What do you mean by "synonym"? Are you saying that two of the three tags should be abolished, and only one kept? Or do you mean that the three tags should all be kept but should be considered interchangeable?
Certainly the field of combinatorics includes an immense amount of subject matter besides permutations and combinations, much of which has nothing to do with counting. On the other hand, permutations and combinations are taught in elementary courses in which the word "combinatorics" is most often never mentioned. Therefore it seems to me to be useful to have separate tags. And, as was mentioned in 40 votes' answer, permutations are important in noncombinatorial mathematics.