Anywhere, in any order or position on the guitar that you can find and play the notes C, E and G you are playing a C major chord. You can double or triple the notes. For example, two Cs, an E and two Gs like you mention.

Originally Posted by: Mick JI know that this is still a C major chord although it might be some kind of an inversion but the positioning seems more natural to me and the chord sounds fuller.[/quote]
The precise term for what you have there is a different voicing of the C major chord. We have and use different voicings to achieve different sounds for different purposes.

An inversion is more precisely when the chord has a different bass note.

See here:
http://www.guitartricks.com/tutorial.php?input=148
[QUOTE=Mick J]
So can I still use this formation, will it impede my progress on the lessons on here or should I change now?

You can and should use that C major voicing. You can and should learn and use many, many more voicings of the C major chord.

Look here for ideas on how to accomplish this goal:

http://www.guitartricks.com/tutorial.php?input=383
http://www.guitartricks.com/tutorial.php?input=389
http://www.guitartricks.com/tutorial.php?input=378
http://www.guitartricks.com/tutorial.php?input=450
http://www.guitartricks.com/tutorial.php?input=464