Combinatorics and Graph Theory

Rencontres for Equipartite Distributions of Multisets of Colored Balls into Urns

Authors: Richard J. Mathar
Comments: 7 Pages.

A multiset of u*b balls contains u different colors and b balls of each color. Randomly distributing them across u urns with b balls per urn, what is the probability that no urn contains at least two balls of a common color? We reduce this problem to the enumeration of u X u binary matrices with constant row and column sum b and provide an explicit table of probabilities for small b and u.
Category: Combinatorics and Graph Theory