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In-Depth Information
Fig. 7.3
Gauss's distribution. M denotes the mean. More than 68% of the values is within a
radius σ
centered on M; more than 95% is within 2σ , and more than 99% within 3σ
7.3
Allocations and Partitions
In the following we consider other important kinds of allocations and some kinds of
partitions, which are special cases of allocations where cells are assumed undistin-
guishable and no cell is empty.
7.3.1
Multinomial Coefficients
If in the formula of binomial coefficients by means of factorials we put at denom-
inator the product of
m
factorials such that
k
1
+
n
, we get the follow-
ing formula for
multinomial coefficients
, related to the Boltzmann distribution in
physics (of the fractional numbers of particles in a gas having some energy levels):
k
2
+
...
k
m
=
n
n
!
k
1
!
k
2
!
=
k
m
!
.
k
1
,
k
2
,...,
k
m
...
