<Dd> n! ≈ (n e) n 2 π n, (\ displaystyle n! \ approx \ left ((\ frac (n) (e)) \ right) ^ (n) (\ sqrt (2 \ pi n)),) </Dd> <P> then the expected total gain will be </P> <Dl> <Dd> 2 m − n _̄ ≈ 2 n π, (\ displaystyle (\ overline (2m - n)) \ approx (\ sqrt (\ frac (2n) (\ pi))),) </Dd> </Dl> <Dd> 2 m − n _̄ ≈ 2 n π, (\ displaystyle (\ overline (2m - n)) \ approx (\ sqrt (\ frac (2n) (\ pi))),) </Dd>

Gas particles moving through air due to random motion