It has been known that the transition probability of the single species ASEP with N particles is expressed as a sum of N ! N -fold contour integrals which are related to permutations in the symmetric group S N . On other hand, the transition probabilities of the multi-species ASEP, in general, may be expressed as a sum of much more terms than N !. In this paper, we show that if the initial order of species is given by 2then the transition probabilities can be expressed as a sum of at most N ! contour integrals, and provide their formulas explicitly.