  We determine, within 1, the value of N for which sum (s1 choose i)(s2 choose
N)(s1 choose N-i)(N choose i) achieves its maximum value. Here s1 and s2 are
fixed integers. This problem arises in studying the most likely value for the
size of the union of A, B, and C if A and C are disjoint sets of size s1, and B
is a set of size s2. Attempting to remove the 1 unit of indeterminacy leads to
interesting conjectures about a family of rational functions.
