In (1), we argued that bias removal is the main underlying idea of both the time reversal reaction balance and maximization of ln of the number of permutations of a set { n(ei) }, (proportional to what is called entropy) subject to Sum over i n(ei) = N and Sum over i ei n(ei) = E approaches to obtaining the Maxwell-Boltzmann (MB) distribution. Furthermore, the removal of bias (independence of n(ei)’s) approach only holds for very large n(ei) values and requires the introduction of a drastic approximation for n(ei)! approx= n(ei) power n(ei). Even though this follows from Stirling’s approximation, it is still a drastic approximation of a factorial function, but is what is required to remove bias, which may be described by n(ei)n(ej) = n(ek)n(el) for ei+ej = ek+el. In (2), we argued that one may find the MB distribution solely from momentum considerations. If this is the case, one would expect that bias must again be removed, i.e. n(p1)n(p2) = n(p3)n(p4) if p1+p2 = p3+p4 (vectors) and that if any factorial expressions appear, a large n(p)! drastic approximation is required. We argue that momentum considerations (even in one dimension) are interesting because one may have n(p) and n(-p) and these should have the same value. Thus, momentum is a vector, but one cannot have its sign appear in n(p). Thus, one would expect some kind of p dot p expression, as noted in (2) or a factorial invariant under v→-v. Now, the n(ei) approach yields p(ei) = C exp(-ei/T) where ei= p dot p /2m and so one may wonder if one may have an independent even function of p for n(p). Rather, it seems that n(p) being even in p should yield the same n(ei) given the relationship between p and e=kinetic energy (nonrelativistic). Thus, a momentum treatment of the MB case should yield probabilities P(p1)P(p2) = P(p3)P(p4) for p1+p2 = p3+p4 (one dimension here for simplicity), but at the same time P(p1) should be even in p1 and should essentially capture n(ei) = N C exp(-ei/T). In the momentum case, this means one should obtain exp(- .5m v dot v/T) which is a Gaussian. Given that one anticipates a factorial expression (as ln(N!/ Product over i n(ei) !) appears in the n(ei) case), this momentum linked factorial expression must be invariant under p → -p and should reduce to a Gaussian for large factorial argument values. We argue that these conditions are met by the Galton board expression discussed in (2). This factorial expression is invariant under the interchange of k and (n-k), where v = k (dv) + (n-k) (-dv), but that v→-v under such an interchange. The large k, n-k renders the probability into a Gaussian which removes bias P1(pi)P1(pj) =P1(pk)P1(pl) for pi+pj = pk+pl (one dimension), but this function is the same as p(ei) as anticipated.