  Thermal states of light are widely used in quantum optics due to their
correlation properties. As is well known, their correlation properties and the
photon number distribution as a whole are strongly dependent on the mode number
selected by the detection scheme. The same changes can be caused by photon
subtraction. Therefore, we describe the general case of the multimode thermal
state after a multiphoton subtraction, when the photon number statistics is
registered by the detector selecting a part of the initial modes. We present an
analytical form of the obtained photon number distribution and its general
properties and check them in the experiment.
