Using Color-Coding and exporting to a GEDCOM file you can determine how many descendants an individual has.
1. Highlight the ancestor
2. Go to Tools>Color Code People
3. Set Color and Select "Descendants of current person". Make sure "Include spouses" is unchecked.
4. Click "Ok"
5. Go to File>Export
6. People to export "Select from a List"
7. Click "Mark group"
8. "Select people by data field"
9. Select "Color coding" and the color the descendants were highlighted.
10. Click "Ok"
11. A pop up window will tell you how many individuals were marked. This is the count for all the descendants of the individual. The primary individual was included in this count so you will need to minus one.
12. There is no need to complete the GEDCOM creation. You can cancel out of the remaining screens.
You can also use Reports > Lists > Statistics List, then mark the descendants of the person. You will get the count, etc broken down by total, male, female, ages, etc.