The statistics employed by quantum mechanics come in two varieties, both strikingly non-classical. (Technically the following results are part of relativistic quantum mechanics.) Particles such as protons and electrons obey Fermi-Dirac statistics and thus the Pauli exclusion principle. These lead to the impenetrability of matter and its ‘space-filling’ character, as well as such chemical properties as valency and color. Particles such as photons and gravitons obey Bose-Einstein statistics and carry the fundamental forces in nature, such as electromagnetism and gravity. See the discussion in Russell, "Quantum Physics."