THE NUMBER OF COMBINATIONS
The combinations of N objects taken K at a time are the possible choices of K different elements from a set of N objects. The number of combinations, which we denote by NCOMB(N,K) is
NCOMB(N,K)=(N*(N1)*...*(NK+1))/FACT(K)
NCOMB(N,K)=0 for N<K
NCOMB(N,K)=0 for K<=0
the following formula holds for all integers K NCOMB(N,K)=NCOMB(N,NK)
IMPLEMENTATION
Unit: internal function, external function without procedure statement
Parameters: integers N>=0,K
Interface:
the FACT function
Returns: the number of combinations NCOMB(N,K)
NCOMB: procedure
parse arg N, K
if K < 0  N < K then return 0
if K = N then return 1
if K > N  K then K = N  K
Nom = 1
do J = N  K + 1 to N; Nom = Nom * J; end
return Nom / FACT(K)

CONNECTIONS
