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*(N-1)*...*(N-K+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,N-K)

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 = N
do J = N - K + 1 to N - 1; Nom = Nom * J; end
return Nom / FACT(K)

 

CONNECTIONS


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last modified 7th July 2014
Copyright 2000-2013 Vladimir Zabrodsky
Czech Republic