Probabilistic Proofs of a Binomial Identity, Its Inverse, and Generalizations
Michael Z. Spivey · American Mathematical Monthly · 2016
We give elementary probabilistic proofs of a binomial identity, its binomial inverse, and generalizations of both of these. The proofs are obtained by interpreting the sides of each identity as the probability of an event in two different ways. Each proof uses a classic balls-and-jars scenario.