Abstract
In this paper, we consider the totally asymmetric simple exclusion process (TASEP) with second class particles that consists of k first class particles and N − k second class particles. We assume that all first class particles are initially located to the left of the leftmost second class particle. Under this assumption, we find the probability that the first class particles are at x, x + 1, …, x + k − 1 and these positions are still to the left of the leftmost second class particle at time t. If we additionally assume that the initial positions of the particles are 1, …, N, that is, step initial condition, then the formula of the probability does not depend on k and is very similar to a formula for the TASEP (without second class particles) with step initial condition.