Selecting points from a list to plot in RStudio

So I have a list of that is at least 1,000 points large that I'm plotting to fit data to. I want to be able to plot either say 15 random points from this list onto the plot or plot something like every tenth point. I'm not sure the best way to go about selecting a specific rows of data.

Say my list is dsc(1:20). How would I manage to plot every 3rd point or to pick 6 at random and plot them. Right now I have too many points on a graph that it makes a poor image for publication.