The maximum negative hypergeometric distribution

An urn contains a known number of balls of two different colors. We describe the random variable counting the smallest number of draws needed in order to observe at least $c$ of both colors when sampling without replacement for a pre-specified value of $c=1,2,\dots$. This distribution is the finite sample analogy to the maximum negative binomial distribution described by Zhang, Burtness, and Zelterman (2000). We describe the modes, approximating distributions, and estimation of the contents of the urn.