**Update**

I was reading the comments to the question, and found that @Kuba had already provided the following answer. I think it's the cleanest solution, so it deserves to be an answer, but please credit him with the idea.

Another idea is to use [`PatternSequence`](http://reference.wolfram.com/language/ref/PatternSequence):

	ClearAll[f]

	f[PatternSequence[a_,b_,c_]?NumericQ] := a+b+c

Examples:

	f[1,2,3]
	f["a",2,3]

>6

>f["a", 2, 3]