On the number of nearly perfect matchings in almost regular uniform hypergraphs (Q1817560)

\textit{N. Pippenger} and \textit{J. Spencer} [J. Comb. Theory, Ser. A 51, No. 1, 24-42 (1989; Zbl 0729.05038)] showed the existence of a nearly perfect matching in almost regular uniform hypergraphs satisfying certain conditions. \textit{D. A. Grable} and \textit{K. T. Phelps} [J. Comb. Des. 4, No. 4, 255-273 (1996; Zbl 0911.05028)] showed that such hypergraphs have exponentially many nearly perfect matchings. In this paper the authors present a simple proof of Grable's extension of Pippenger's theorem based on a comparison of upper and lower bounds of the probability for a random subgraph to have a nearly perfect matching.