function bincoeff=bincoeff(n,r)

% Calculates the binomial coefficient which represents the number of
% possible orders of drawing exactly r red balls in n draws.
% Tomas Olofsson. Dec 2004

if r<0
  bincoeff=0;
  return
end
if r>n
  bincoeff=0;
  return
end
if n<21 % If n larger, we will have some difficulties with the precision.
  bincoeff=factorial(n)/(factorial(r)*factorial(n-r));
else
  bincoeff=1;
  % A loop in which the computations are organized to avoid overflow.
  for k=r-1:-1:0
    bincoeff=bincoeff*(n-k)/(1+k);
  end
end