I have a raster file with two bands and a vector shapefile. I used raster extraction by mask and created the desired area. Now I want to calculate the number of pixels for Band 1 and Band 2 of the new clipped mask file. What would be the best way to do that?

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Use Menu Processing / Toolbox / Zonal statistics, set your polygon layer as well as your raster layer as input and at Statistics to calculate select count. Run the tool. In the attribute table of the resulting layer, you find the number you're looking for.

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