factorial(n) lfactorial(n) choose(n, k, order.matters=F) choose.multinomial(n, m)
choose.multinomial
.
Need not be integer for
factorial
or
lfactorial
.
n
.
factorial(n)
is
n
!
lfactorial(n)
is the natural logarithm
of
n
!
choose(n, k)
is
n
! / (
k
!
(n-k)
!),
i.e. the binomial coefficients.
choose(n, k, order.matters=T)
is
n
! /
(n-k)
!,
i.e. the number of ordered subsets of length
k
from
a set with
n
distinct elements.
choose.multinomial(n, m)
is
n
!/
prod(m
!
)
,
the multinomial coefficients.
These functions use
gamma
and
lgamma
for computations.
factorial(5) choose(5, 2) choose(5, -1:6) choose.multinomial(6, c(3,1,2)) choose(5, 2, order=T)