Randomly select n points within a radius in QGIS

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I have a dataset of 5000 records which I've plotted over an OSM layer using QGIS and I wish to randomly select 50 from within a radius of 2km from a point of my choosing.

It is similar I think to this here where again the Select Features by Radius is almost what I'm aiming for, but unlike the previous question, I only wish to randomly select 50 points from within the 2km radius.

Using the Select Features by Radius, it looks like there would be approximately 300-400 points within any 2km radius. So a solution would have to be able to randomly select only a fraction of these.

Thanks!



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