  Let $K_n$ denote the number of distinct values among the first $n$ terms of
an infinite exchangeable sequence of random variables $(X_1,X_2,\ldots)$. We
prove for $n=3$ that the extreme points of the convex set of all possible laws
of $K_3$ are those derived from i.i.d. sampling from discrete uniform
distributions and the limit case with $P(K_3=3)=1$, and offer a conjecture for
larger $n$. We also consider variants of the problem for finite exchangeable
sequences and exchangeable random partitions.
