An adsorbing filter allows gas particles to stick to locations on the filter surface. Once a particle sticks to a location, that location is filled. The filter can no longer remove gas particles when all locations are filled. Each \(1.0 \mathrm{~nm}^{2}\) of the filter surface has six adsorbing locations, each capable of adsorbing one gas particle. In the volume just adjacent to one \(1.0-\mathrm{nm}^{2}\) area, there are 100 gas particles. Each of these particles has a slightly different energy, making each particle unique. In how many ways can these 100 particles adsorb onto the six locations?