1 Greg Kirk[Ki] raised the question of comparing the following two ways for labelling balls. Given r predetermined positive integers n i , (1 ≤ i ≤ r), and given N balls (N large), consider two ways to randomly assign r− component vectors of integers (a 1 ,. .. , a r) to them, such that 1 ≤ a i ≤ n i. We will call these vectors 'labels'. Of course altogether there are r i=1 n i possible labels....