A laboratory is conducting an experiment where a liquid mixture containing particles of various sizes needs to be filtered. The filtration system consists of two filters operated in series. The first filter removes $70\%$ of particles larger than $5$ micrometers $(\backslash$mu m$),$ and the second filter removes $80\%$ of particles larger than $2\backslash$mu m$.$ If the initial concentration of particles larger than $5\backslash$mu m is $1000$ particles per milliliter $($particles$/$ml$),$ and the concentration of particles larger than $2\backslash$mu m but smaller than $5\backslash$mu m is $500$ particles$/$ml$,$ what will be the final concentration of particles larger than $2\backslash$mu m after passing through both filters?