Stroking outside border of an object with holes. {scrn shots}

Question

Probably a really simple fix to this, but I'm still new to Illustrator so any help is appreciated
This is the image that I need to be outlined, but only around the very outside border.
Applied a regular stroke:
Grouped it with another part that also needs outlining on just the outside edge, and tried using a method I saw on here:
and the results:
Sort of helped but not really for what I'm looking for. If anyone could help my out, again it'd be much appreciated.

Answer 1

Fisheye,
As I (mis)understand it, you may:
1) Select the whole group and copy it, then work with the copy;
2) Ungroup and then with everything selected either just Pathfinder>Unite or Object>Compound Path>Release and Pathfinder>Unite to get one simple path with the outer shape;
3) Give the path the desired Stroke and no fill.
You may move the stroked path down beneath the original artwork (and use twice the desired stroke) if you want the stroke outside the original filled shape, or depending on version you may set the Stroke to be outside.