  Remixed Eulerian numbers are a polynomial $q$-deformation of Postnikov's
mixed Eulerian numbers. They arose naturally in previous work by the authors
concerning the permutahedral variety and subsume well-known families of
polynomials such as $q$-binomial coefficients and Garsia--Remmel's $q$-hit
numbers. We study their combinatorics in more depth. As polynomials in $q$,
they are shown to be symmetric and unimodal. By interpreting them as computing
success probabilities in a simple probabilistic process we arrive at a
combinatorial interpretation involving weighted trees. By decomposing the
permutahedron into certain combinatorial cubes, we obtain a second
combinatorial interpretation. At $q=1$, the former recovers Postnikov's
interpretation whereas the latter recovers Liu's interpretation, both of which
were obtained via methods different from ours.
