During the beach tutorial I created stamp border for the illustration. Here is the step-by-step on how to get there.
The reason for ungrouping and combining the circles first lies in the restriction in Inkscape to only do a Union, Difference, Intersection, Exclusion or Division between two objects.
Tools like CorelDraw can do these with a group or even just several selected objects. Try around around a little see how your vector application handles these very handy commands.