custom GIS program using ESRI ArcObjects in c#

I'd like a tool that will create points within a selected polygon. This is for creating forest inventory plots on a property. Instead of manually delineating the points (with bias), I'd like a random point generator tool. A polygon will be selected, click the add-in tool button, it will ask how many points are needed. The tool will generate random points within the polygon and create a new point shapefile with lat/long coordinates in the attribute table. Deliverable will be an ArcMap add-in tool that creates a specified number of randomly placed points within a polygon.