Scattering by a sphere with a different internal structure has drawn attention. The forward scattering light of a water droplet containing multiple different size carbon inclusions is calculated by the finite-difference time-domain method. Herein, distribution of these carbon inclusions conforms to Apollonian packing in a droplet. The space left over between carbon inclusions constructs a fractal, of which the fractal dimension D is expressed as $D\approx 1.305684$ . The incident wave is in the y-direction polarization. The results show that the amplitude of the intensity fluctuations is not associated with the fractal dimension. Carbon inclusions only decrease the component y of electric field intensity at the place of inclusions. For a droplet containing multiple concentrated inclusions with different sizes, the amplitude of the intensity fluctuations is related with every space between inclusions. And the far field light intensity approaches the intensity caused by one carbon inclusion as space between inclusions becomes less and less. In order to know the effect of polarization direction, transmissibility versus θ(angle between the polarization direction of the incident wave used and the y-axis direction) is finally obtained. It can be seen that the transmissibility changes with θ conformably and reaches a minimum when $\theta =30°$ . Transmissibility is equal for $\theta =90°$ and $\theta =0°$ .