you can do that with dependent filters:

'For advanced usages, you can also bind controls to other controls to establish 
chains of dependencies.'

  dashboard.bind(countryPicker, regionPicker).bind(regionPicker, cityPicker);

Find the documentation here:
https://developers.google.com/chart/interactive/docs/gallery/controls#6-establish-dependencies

at the end of the part 6

If you chain category filters you will have the desired result.

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