I do as, Select the first item in folder > Hold SHIFT key > Select the last item in folder > CTRL+C.
It will show the total count of copied items in the clipboard icon usually located at the right bottom corner of TC.
Testing: NX 10 | NX 11 | Teamcenter-NX Integration
Teamcenter 11.2 | TC Vis 11.3 | Active Workspace 3.2
As a alternative, i use below option.
1. Select the 'Solution Items' folder and go to 'Details' tab. The tab shows the list of objects under 'Solution Items' folder.
2. In the right corner, select 'Print Table' --> HTML/Text.
3. In the resultant window, you can see the object count just above the table.