etc. (after a list?)

[pinkie9]

This is about "etc." Dictionaries say that "etc." is used after a list to show that there are other things that you could have mentioned.
How many words are required to form a list before "etc."? At least two? Three? I mean,

1. The children can take part in music, dance, paintings, etc.
2. The children can take part in music, dance, etc.
3. The children can take part in music, etc.

I understand 1 is correct, but how about 2 and 3?
I sometimes see sentences like 2 or 3 written by native speakers. Maybe what the dictionaries say is old-fashioned?

 

[probus]

2 is okay in my opinion. In the case of a single item "list" as in 3, it depends on how obvious it is from the context what other items belong in the list. If the context makes that obvious, 3 is okay and that is why you see such constructions by native speakers.