# NOT FINISHED YET !!!!

# define a factorial function
# gives 1 for negative values as well
define f(x) {
  if (x>1) {
    return (x * f (x-1))
  }
  return (1)
}

# determine how many combinations would be dis-allowed
# from a cardinality constrained powerset
# given unitary state failure mode conditions
define uc(c,k,x) {
 aa = 0;
 #for(i=2; i<=c; i++)  aa += k * f(k)/(f(i)*f(k-i));
 if ( c>2 ) {
	return aa + uc(c-1,k,x);
 }
 return aa;
}

# cardinality constrained powerset
# how many combinations of cardinality k
# can we have from c number of components
# with x number of failure modes
define ccps(c,k,x) {
 return f(k*x)/(f(c)*f(k*x-c))
}



define us(c,k,x) {
	a=0;
	for(i=1;i<=c;i++) a += ccps(i,c,x);
	# a now holds all combinations 
	# we must now subtract those combinations
	# dis-allowed under unitary state conditions.
	a -= uc(cc,c,x);
	return a;
}


us(2,3,3);