ABSTRACT
A
k
= fa
; a
; : : : ; a
k
g that belongs to C
k
(W
n
) we uniquely correspond the
set of its permutations P
k
(A
k
), which is a subset of P
k
(W
n
). Note that
P
k
(A
k
) and P
k
(B
k
) are disjoint sets for A
k
and B
k
dierent k-combinations
from C
k
(W
n
) and also that each k-permutation from P
k
(W
n
) belongs in
one of the sets P
k
(A
k
), A
k
2 C
k
(W
n
). Thus, the set fP
k
(A
k
) P
k
(W
n
) :
A
k
2 C
k
(W
n
)g constitutes a partition of the set P
k
(W
n
). Further, accord-
ing to the denition of a permutation, N(P
k
(A
k
)) = N(P
k
(W
k
)) for every
A
k
2 C
k
(W
n
) and so, by the addition principle,
N(P
k
(W
n
)) =
X
A
k
2C
k
(W
n
)
N(P
k
(A
k
)) = N(C
k
(W
n
))N(P
k
(W
k
)):
At the second stage we enumerate the number P (n; k) = N(P
k
(W
n
)) of
k-permutations of the set W
n
and conclude the number P (k) P (k; k) =
N(P
k
(W
k
)). Then the number C(n; k) = N(C
k
(W
n
)), of k-combinations
of the set W
n
, is obtained as C(n; k) = P (n; k)=P (k). This technique has
been employed for the derivation of this number in Theorem 2.5.
